Both teachers need to have a re-think. There's no 'correct' way anyway. We each find our own depending on our fingers, their strength, and where we are on string/fret, and where we are going next, also considering where we were before. All that lot means no two situations and no two players will do the same. The right way is the best way for each player in each circumstance.
Having said all that, it also depends - heavily - on which string, which fret, and how wide a bend. Let's take that 12th fret bend. Which string? We don't know, but that matters. Let's say top string. It greatly depends on where the previous notes were, and where the next will be. If the next ones are higher, I'd advocate index or middle. If they go down again, ring or pinky could do the job.
HOWEVER - what bend is it - 1/2 a fret, 1 fret, 2 frets? Again, we don't know - that makes a big difference. A bend of a semitone or more doesn't need 3rd or 4th finger - it needs both - or even 3 or 4. And with bigger bends, it's not the fingers that do the work as much as the hand. Use 3 or 4! Fingers are only there as an extension.
If this comes as a minirant - it might be! Too often teachers give sweeping statements, when there's no simple answer - hence mine.The question really ought to be pointed at both teachers, and reasons expected. I want my students to question everything I say, and if I can't justify it, to their satisfaction, I really shouldn't have said it.
Dvers - please be kind enough to specify your reasons!