You need an M-1 visa to train for a standalone FAA PPL in the USA, because the TSA say so. You won't find it in US law, because it is an administrative rule, not law.
I just checked the
www.flightschoolcandidates.gov website, and the official "Final Interim Rule" that's on there (as a pdf file). It only mentions that the candidate needs "a passport and a valid visa" but there is NO mention that the visa has to be an M-1. I did not login and do a dummy application but I found a description of that process which mentions a "drop down" box which allows you to select your visa type (A-1, A-2, B-1 etc.)
So if you have a reference that the visa needs to be an M-1 visa, I'd appreciate it.