My understanding of the situation is:
If its a BFR then you need neither TSA clearance or a visa.
If its the check ride and oral exam for the issuance of the initial licence, IR or ME then you need TSA clearance and an M1 visa. Whilst for some courses that have less than 18 hours of tuition a week you can use the VWP, flight training is not one of them!
If you have TSA clearance for the flight school you are using, then they may be able to let you know if they expect you to have a visa. But definately give the embassy a call and ask them!
When you have an answer post it back here - or even better add it to the knowledge in BackPackers USA training thread.