Originally Posted by Flyhayes

There is nothing that determines what constitutes professional flight training. I've trained several commercial students under this provision and never had a problem with TSA or ICE. Nowhere does it state that a tourist visa, or person traveling under the visa waiver program is excluded from "professional" flight training.

Originally Posted by Flyhayes

There are a few (2 still in operation, if I recall correctly) part 142 GA flight schools (i.e. not turbine/large aircraft training centers) as I mentioned these were granted due to a loophole that the FAA has since closed.

You are correct, in that there are some part 141 schools that do have examining authority (I had missed that part).
However, unless the rules have recently changed, 141 flight schools that do not have in house examiners can not count a failed check ride as a training event. A 141 course completion and a check ride are two completely different things. In my opinion, I think the following references pretty clearly excludes schools without examination authority.

§141.73 Privileges.

(b) A pilot school that holds examining authority for an approved training course may recommend a graduate of that course for the issuance of an appropriate pilot, flight instructor, or ground instructor certificate and rating, without taking an FAA knowledge test or practical test, provided the training course has been approved and meets the minimum ground and flight training time requirements of this part.

§141.77 Limitations.
(a) The holder of a pilot school certificate or a provisional pilot school certificate may not issue a graduation certificate to a student, or recommend a student for a pilot certificate or rating, unless the student has:

(1) Completed the training specified in the pilot school's course of training; and

(2) Passed the required final tests.