1 I don't see the mandative element in your sample sentence. The speaker is, I assume, using 'claim' to mean that the original speaker stated the stuff about wedding rings as a fact; I can't see a suggestion or command there. If someone proclaimed this, as a way of ordering the use of gold from that date on, it would be different, but in this sentence, the verb is not being used in a way like claiming a reward, etc, though off-hand, I can't think of a way of turning this other into a sentence with the form you're after. I should probably mention that I am a British English speaker and rarely use the present subjunctive, but even the 'should be' wouldn't work for me.
2 It's not a term in very wide use but, for my money, any verb that meets the criteria can be termed as such. In a wider sense, I believe that if a word, phrase, etc, meets the definition laid out for any grammatical term, then it's fair to include it. If it's a verb, mandative and triggers the subjunctive among English variants that use the subjunctive, then who has the right to say it cannot be included because there is an exclusive list and it is not on it?
Student or Learner