I agree with what you say about the TSA assessment, however the AFSP website says
All other training events (other than initial certificate, IR or MEL) on aircraft with MTOW of 12,500 lbs. or less are exempt from AFSP regulations, including Commercial Pilot License (CPL), Airline Transport Pilot License (ATPL), and Certified Flight Instructor (CFI). These events are exempt only if the candidate holds an FAA stand-alone pilot certificate.
But it's not a big deal anyway, and I will contact them to argue my case.
The main hassle is the visa.
no sign off is required from a CFI for the initial check ride
Shall I understand that I don't need a visa because no training is formally required?
So basically if I fly with an instructor without him signing anything, it would be no different than me flying with him just as a "refresher" or as some instruction on the type (since I already hold an FAA PPL).
Thanks