What a coincidence, VJW! I was at an FAA Safety Team CFI conference yesterday and the head of the TSA vetting department was there to talk about foreign national background checks. In short, if you're not a US citizen you need the TSA check for:
* the first issue of a pilot licence, but not subsequent licences eg get TSA vetted for a PPL, won't need to do it again for CPL or ATP. The piggy back PPL doesn't count as a prior certificate.
* Instrument rating
* Multi engine
* Every type rating ie aircraft above 12500 lb
So, from the info. you gave you would need the background check.