I was under the understanding that Teachings of Holy Mother Church is the couple to be husband and wife are the sacrament and the priest is the witness.
Yes, the couple are the ministers of marriage in Catholic theology, but the sacrament of marriage also requires jurisdiction for validity. (The sacrament of penance also requires a jurisdiction for validity called "faculties".) Jurisdiction is either ordinary, delegated, or supplied.
Canon 1094 (1917 CIC for the Latin Church) says that only those marriages are valid which are contracted before the pastor or local ordinary [ordinary jurisdiction] or a priest delegated by either [delegated jurisdiction], with 2 witnesses (and following other rules the Church specifies for validity), with exceptions given in canons 1098 [supplied jurisdiction] and 1099. These requirements are part of the "canonical form" of marriage, which is required of Catholics, though dispensations can also be granted.
Canon 1098 says that if the pastor or ordinary cannot be approached without grave inconvenience, then in danger of death, marriage is valid and licit before witnesses only. Likewise if the inconvenience is foreseen to last more than a month. This canon also says that if a priest is available (not one with ordinary or delegated jurisdiction), he should assist at the marriage, though it is valid before only the witnesses.
Historically, this covered people living far away from a church who might only see a priest a couple times a year.
It is my understanding that the SSPX used (among other things) the "grave inconvenience" provisions of Canon 1098 for supplied jurisdiction of marriages. The 1983 CIC has almost identical provisions, so this shouldn't be a problem. In practice, however, conciliar annulment boards haven't always agreed with the SSPX's supplied jurisdiction, and so may see a defect of canonical form and grounds for an annulment.