Student or Learner
I think it's important. 'What' is correct because there are no criteria identified yet. It hasn't been established yet whether the criteria are limited.
'Which' would be correct if you were given a list of criteria, only some of which we should use to determine reliability.
I also agree that the explanation you have given is correct. However, many, many native speakers do not observe this difference, at least in British English. I am always reluctant to insist that learners follow rules that native speakers don't.