I was talking to a lawyer once—not a canon lawyer—and he made the comment that, with respect to civil cases, a lawyer’s job is to clean up other people’s messes.
It’s sort of the same with tribunals. People make all kinds of messes when it comes to marriages or attempted marriages, and the tribunal is expected to clean it all up so everybody can move forward.
But really, the tribunal has only one job: to determine whether a valid marriage existed from the beginning. What happened after the marriage was contracted has no direct bearing on the validity of the marriage, although it may provide evidence of the couples’ state of mind at the time the vows were exchanged. The Church has no authority to invalidate a valid marriage. It does not issue annulments. It issues declarations of nullity declaring that the evidence is that there was no marriage from the beginning.
And both parties to a marriage may not agree as to whether it was valid or not. I recall one guy whose wife had filed for an annulment telling me that he intended to fight it all the way, because in his view, the marriage was valid from the beginning and there were no grounds for filing it null.
And there have been some cases in which a local tribunal grants a decree of nullity, which is then appealed by the other party to the Apostolic Signatura, which might uphold the validity of the marriage.
Yes, the tribunal always should work to discover the truth, in charity, but it must find the truth.