Huh, I too have never noticed that dative and am now curious as to how its functioning? I think your friend is right that it is not the subject of the infinitive but I still think we may have a mystery on our hands. The dative is a feminine pronoun and we would need to confirm the referent.  Did your friend say why he thought it would refer to the prophets when the pronoun is feminine (remember prophet is one of those tricky masculine nouns that has 1st declension endings)? The closest plural feminine noun is "the churches" in the previous clause, so that might be the most probable referent. That would put us back where we started so that the second clause in vs34 should be "for they are not allowed to speak in/to them (the churches)."  I think that might be the best translation at first glance but I always reserve the right to change my mind upon closer analysis when datives and pronouns are in the mix!

 All that said, I think your point is a valid application either way you translate it. It also fits with Matthew 19 where in a confrontation you should take another along with you to approach someone.......  Bu may not affect the student/teacher scenario since its not technically within the church setting.