Interesting, I knew that baptism and matrimony did not require a valid minister but I am unsure of the details (for matrimony). So lets assume that a man wishes to marry a 16yr old girl,, she agrees, both parents agree, the government says no (though can legally fornicate in most western nations/state) and the SSPX says no. How would a valid marriage work here? Also why then does the SSPX like to brag about having 'authority' to have confessions and marriages if you can marry without a priest?
The man and woman being married are the ministers of the sacrament of matrimony. Canon law allows marriage to be contracted without the presence of a priest if no priest will be able to be present within one month. To your question, I believe the state would have no right to forbid that marriage. That contradicts ecclesiastical law as Canon law gives the ages of 16 for men and 14 for women as minimum ages for entering into a valid marriage, and the parents of the girl consent
1. Only the supreme authority of the Church declares authentically whenever divine law impedes or invalidates marriage.
§ 2. It also belongs exclusively to the same supreme authority to constitute, through either universal or particular law, other impeding or diriment impediments to marriage for the baptized
If the SSPX refused, the couple should try other trad groups. If they all refused, I think they would be able to validly and licitly marry, in the presence of witnesses only, according to Canon 1098