Its not clear if training for a US rating OUTSIDE the US is covered by this...
It is clear. If you read the rules:
http://www.tsa.gov/interweb/assetlib...lien_Pilot.pdf
the intention is cover those schools and individuals providing training outside the US.
Of course, a loophole exists in the form of the FAA's general acceptance of instruction provided by non-FAA ICAO-licensed instructors. Typically, only 3 hours prior to a checkride (given in the last 60 days) are required from an FAA instructor. [this various with the certificate being applied for]. Overseas instructors with non-FAA instructor ratings will be still be OK to provide instruction. The student will however at some point need to be registered with the TSA when he/she finally receives those last 3 hours and flies the checkride.
Ground Instruction is exempted, as are BFRs and Instrument Proficiency Checks. For this, see:
http://www.tsa.gov/interweb/assetlib...Exemptions.pdf