The canonical excommunication incurred by reason of the illicit ordinations was lifted from the Bishops, but there remains the sacramental one, de facto, for the schism: They have distanced themselves from [being in] communion with the Church.
CM: First, does the SSPX have extraordinary jurisdiction to absolve sins?
MB: SSPX priests are presumed at Universal Law only to possess jurisdiction or the faculty to absolve from sin in two exceptional circumstances. First, pursuant to the norm of can. 976, "Any priest, even though he lacks the faculty to hear confessions, can validly and lawfully absolve any penitents who are in danger of death, from any censures and sins, even if an approved priest is present." "Any priest" according to this norm would include validly ordained SSPX priests. Second, in conformity with the norm of can. 144, § 1, whenever (1) Common Error of Fact or Law and (2) Positive and Probable Doubt of Fact or Law have been verified to exist in a certain fact pattern, the Church "supplies" a iure universali the faculty required for SSPX priests to absolve from sins validly. "Error" in this norm means a state of erroneous judgment; "doubt" in this canon means a grave, positive and probable doubt asserted by numerous doctors of Canon Law of unimpaired reputation extant on the part of the SSPX priest acting as confessor.
While canonists find no controversy in the assertion that SSPX priests who are validly ordained and not otherwise impeded have the faculty to absolve the faithful from sin in danger of death of a penitent (cf. can. 976), the jurisprudence of the Roman Rota does provide some rare official light into the other question of whether SSPX priests possess the jurisdiction required to witness marriage validly.
The Tribunal of the Roman Rota has issued, per my count, five judgments declaring the nullity of marriage of those faithful who exchange vows before an SSPX priest. The legal rationale for such judgments has been the ground of Defect of Canonical Form (cf. can. 1108).
The Code of Canon Law states:
Only those marriages are valid which are contracted in the presence of the local Ordinary or parish priest [pastor] or of the priest or deacon delegated by either of them, who, in the presence of two witnesses, assists ... . (cf. can. 1108, § 1)
In layman's terms, this means that if a Catholic couple exchange vows between each other before any priest who has not received delegation from an authority indicated in the canon, or the supply of said faculty by operation of can. 144, then such a marriage is presumed to be invalid according to the norms of the Code of Canon Law.
Whenever these norms have been applied to cases where an SSPX priest witnessed the exchange of vows of two Catholic faithful appearing before him, the Judges of the Roman Rota, the Catholic Church's universal court of appeal, have, to my knowledge, without exception, always declared such marriages to be utterly null and void. An abstract of just such a judgment was released by the Roman Rota in 2010 (my translation):
An affirmative sentence has recognized the nullity of marriage by reason of defect of delegation in the celebrating priest belonging to the "Society of Saint Pius X" (the so-called Lefebvrians). According to the panel of judges [Turnus], on the part of the faithful who follow schismatic pastors — as an aside, the Lefebvrian community is qualified as dissident but not separated from the Church — one cannot automatically presume the will to defect from the Catholic Church (from the moment that their choice could have been influenced more by liturgical preference than by the refusal of papal authority) and therefore these [individuals] remain bound by canonical form (can. 1117 in the text preceding the reform introduced by the Motu Proprio Omnium in mentem of 26 October 2009; A. 95/09).
This jurisprudence of the Roman Rota is entirely consonant with the decision of Pope St. John Paul II in 1988 to grant to the Cardinal President of the Pontifical Commission Ecclesia Dei the faculty to sanate in radice marriages witnessed by SSPX priests: "b) sanandi in radice matrimonia nulla ob defectum formae can. 1108 requisitae, coram iisdem Sacerdotibus celebrata," translated: "b) of sanating in radice marriages null by reason of defect of form required by can. 1108, celebrated before the same Priests."
CM: Second, does the Pope's act confirm that the SSPX normally does not have faculties to absolve sins?
MB: Apart from the circumstances foreseen by canons 976, 144 and the temporary circumstances described in the letter written by Pope Francis on 1 September 2015 to Archbishop Rino Fisichella, President of the Pontifical Council for Promoting the New Evangelization, SSPX priests do not ordinarily possess the faculty required to absolve a faithful validly from sin.
CM: Pope Benedict in his 2009 motu proprio made clear the SSPX has "no canonical status" in the Church and exercises "no legitimate ministry." But SSPX supporters cite Cdl. Darios Castrillon Hoyos, who said the SSPX has "irregular canonical status." Is there a difference between no canonical status and irregular canonical status?
The explanatory Nota issued by the Secretariat of State of the Holy See on 4 February 2009 (AAS CI  145-146) states, more precisely, the following (English translation mine):
The loosening of the excommunication has freed the four Bishops from a most grave canonical penalty, but it has not changed the juridical situation of the Society of Saint Pius X, which, at the actual moment, does not enjoy any canonical recognition within the Catholic Church. Also the four Bishops, even though they be loosened from excommunication, do not have a canonical function within the Church and do not exercise a ministry in her legitimately. (italicization mine)
The above quotation of the Secretariat of State indicates that the Society of Saint Pius X as an entity does not enjoy any recognition of its existence on the part of the Catholic Church from a canonical point of view. This means that the Catholic Church, while perhaps acknowledging its de facto existence according to the norms of Civil Law, does not ascribe any canonical recognition to the Society. As for the Bishops, the Holy See holds that they have not been granted any official munus to fulfill by the Church. Consequently, it follows that any ministry ordinarily exercised by them is not authorized by the Church.
CM: The SSPX admits it is not in full communion with the Church. Some say this language implies they are schismatic. What does "not in full communion with the Church" mean?
MB: The expression connotes that the members of the Society are not in complete harmony with the official teachings and discipline of the Roman Catholic Church. The Society both officially dissents from certain doctrines pronounced by the Magisterium since the Second Vatican Council, and rejects certain disciplinary norms of Universal Law enshrined in the Code of Canon Law promulgated in 1983.
CM: Pope Benedict made clear in 2009 that all SSPX clergy remain suspended a divinis. We understand that means that no clergy are allowed to offer the sacraments publicly under pain of mortal sin. What is the canonical penalty for violating their suspension and offering the sacraments publicly?
MB: Pursuant to the norm of can. 1378, § 2, 2º, an SSPX priest appears to incur a distinct latae sententiae censure of suspension every single time that without the ability to do so validly, he attempts to impart sacramental absolution, or at least attempts to hear confessions outside of the danger of death of the penitent. The multiplication of latae sententiae censures in such a fact pattern is a little-known but operative presumption that is obtained in application of the norms of cann. 1321, § 3 coll. can. 15, § 2.
CM: Does it place the SSPX clergy in mortal sin, or in danger of mortal sin?
MB: Clearly at least in an objective danger of mortal sin, but not just the SSPX priest. Any Catholic faithful who seeks in genere to receive a sacrament from an SSPX priest, and in specie to receive absolution from sins confessed to an SSPX priest outside of the danger of death and the Jubilee Year of Mercy decreed by the Holy Father, per se does not receive validly and licitly the benefit of the sacrament. The norm of can. 1335 cannot be invoked to demonstrate the supplying of faculties to a priest to absolve from sin validly. All that the norm of can. 1335 does is remove pro tempore the canonical prohibition extant on the part of the SSPX priest from celebrating a sacrament, thereby returning a priest under, for example, the censure of excommunication or suspension to the canonical state he was in prior to having incurred the censure. This means that if he did not possess any faculty to absolve from sin before incurring suspension, then he still does not possess such a faculty unless it be given to him by the competent ecclesiastical authority, who normally is the territorial Bishop the SSPX priest finds himself in. For any priest, not just an SSPX priest, to celebrate the Sacred Mysteries illicitly is to risk not just his own spiritual ruin, but that of the individual faithful he attempts to assist, for the reasons that have been expounded.
18 September 2015
Marc Balestrieri, JCL
President and Senior Canonical Counsel
Canonical Aid, Inc.