Hmmm not so sure about that. As soon as l, holder of a FAA cfi, sign the log book, isnt that training
Not if you are a JAA FI in a G-reg. The training is still just as applicable.
Also if you are both an FAA CFI/CFII and a JAA FI then you can always say the training was under JAA. Especially if in a G-reg; having a dual FAA+JAA instructor rating would be practically worthless otherwise.
Also some training is not subject to TSA. Ref:
http://www.aopa.org/tsa_rule/index. This link shows that below 12500lb these requirements apply only to flight training for a recreational pilot (applicable to US only), sport pilot (applicable to US only), private pilot (FAA PPL), instrument rating (FAA IR), or multiengine rating. A BFR, for example, is exempt. Curiously, an existing PPL holder training for a CPL may also be exempt. The moment any training is exempt, it becomes pretty well impossible to label a particular flight as requiring TSA.
There is also the pre - October 2004 exemption for TSA. So a suitable FAA training logbook entry before that date removes the need for TSA. Ref:
http://dmses.dot.gov/docimages/pdf90/300642_web.pdf
Other than the above exemptions, the checkride itself certainly is subject to TSA. However I don't think one has to go through the full TSA process (fingerprints, approved school, etc) if doing it in the UK because (for example) the training establishment is not going to appear on the TSA website pulldown menus.
My own experience, in a school in the USA which was very fussy about the paperwork, is that the TSA compliance of any foreign FAA instruction is not questioned.