University students are supervised by a licensed psychologist professor and it is perfectly fine.
My son just got his testing done at the local university. And they test on a sliding scale fee. I am waiting for the results because they do all the work and then have to present it to the professor (and possibly classmates I am not sure). I signed consent for video taping only for use with her professor (so they go over the video tapes too). So it takes a little longer to get the results but I feel the results will be valid and it should be accepted because the professor signs the report too.
I would think there might be quite a difference if the child tested is a 2E kid since there are so many things that can go wrong and it really needs to be someone with the experience to administer the tests.
