The M1 Visa is a vocational training visa.
The Part 91 training organisation that I use in the US (where I am non-resident) have been through many CBP and TSA audits of their foreign clients, none of whom are under the M1 program with no problems whatsoever. They follow the TSA procedures rigourously.
The argument that seems to be accepted is that a Part 91 PPL and IR for their clients is recreational and not vocational. They do not offer a Part 91 or Part 141 pathway of PPL/IR/MEL/CPL/CFI/ATP which would make their training vocational rather than recreational.
I know that this is an anecdotal recounting of a single data point. The conclusion that I have drawn could also be incorrect.