You can do this with any Part 61 training provider though. Implying that this is JAA training is just marketing thorough peoples lack of knowledge.
You can go to the states and do an FAA PPL with any Mom and Pop flying school, you can then study ATPL distance learning whilst training for FAA Commercial and Instrument, again at ANY Part 61 school, or even with just any old CFI/CFII who happens to have access to an aircraft. When you go back to JAA land to do your conversions, how much JAA flight training have you received? The square root of f... all!!!!
Cheapest on paper will not work out cheapest in the end I'm afraid.