All clerics require faculties to licitly hear confessions. Bishops, however, can validly absolve even while his faculties are suspended, while a priest cannot (except under emergency conditions).
This is only sort of true. Canon 967 § 1 says,
Bishops likewise have this faculty [viz., of hearing the confessions of the Christian faithful everywhere in the world] and use it licitly everywhere unless the diocesan bishop has denied it in a particular case.
So, the thinking goes, these SSPX “bishops” are, sacramentally speaking, bishops, and so they can simply go about hearing confessions at will.
It seems obvious when one looks at the canon, however, that this was written for the everyday governance of the Church, and not for the strange cases of episcopi vagantes and the like. Does one suppose that this canon grants Thuc-line sedevacantist bishops to hear confessions anywhere they want? Or, not to put too fine a point on it, recall that Eastern Orthodox bishops are “bishops” in the same way as the SSPX “bishops” are; does Canon 967 give them, too, faculties to hear Catholic confessions?
Rather, in keeping with the nature of the Code, and in particular Canon 375 –
§2. Through episcopal consecration itself, bishops receive with the function of sanctifying also the functions of teaching and governing; by their nature, however, these can only be exercised in hierarchical communion with the head and members of the college.
– it seems more correct to conclude that the suspended SSPX prelates do not enjoy any sort of de jure faculty in this regard at all, no more than an Old Catholic bishop might.