If you look at section 472 of the Higher Education Act it’ll give you a really good definition. I had to research more than just there to get my answer, which was similar to yours. Please forgive because I now cannot remember each section, article and etc. But that’ll get you on the right path.
Regardless, if I’m not mistaken, to be considered PSEL, the “student” has to enroll and become accepted, they have to receive some form of diploma from that school that they’ll be attending (i.e. Associate, Bachelors, Masters. Etc)
Hope this helps!