There are plenty of FAA CFI/CFII instructors here in Europe. Many are very highly qualified e.g. a friend of mine is a CFII/ATP and A&P/IA.
Even setting aside that the FAA accepts foreign flight training towards all FAA licenses and ratings, there has never been a problem getting trained in Europe with FAA instructors.
Many, being freelance, are available to travel with businessmen/pilots around Europe, in the customer's own plane, thus delivering first class on-the-job training which beats the structured and artificial JAA IR process hands down. Many have turboprop and bizjet experience. One only has to look at the # of new JAA IR holders (and FAA IR holders too, for different reasons) posting questions on the forums on how to fly IFR from A to B... Eurocontrol routings, etc.
The issue has always been with arranging the FAA checkride. This was the case in 2003 when I first started digging around this route (visiting FAA DPEs, or FAA salaried examiners were the only option and were rare as the proverbial rockinghorse s**t, and their travel schedules were even less predictable) and this situation did not improve much in subsequent years. Visiting examiners were stopped by the FAA in late 2007. Few people will write anything else on this topic; many (myself included) have been threatened with lawyers and had all kinds of hassle - as most regulars here know well anyway.
Today, most people just go to the USA, where everything works smoothly, and it is a lot cheaper. The big gotcha is that you won't be doing the checkride in your own plane, which probably wastes a week's flying. Against that you have the big benefit of just getting on with it, with no distractions. The visa/tsa is just a small hassle puts a lot of people off but actually takes up maybe 2 man-days to process.
SoCal - you may be right (this one has been doing the rounds as long as I remember, but the FAA has never ruled on it one way or the other) but it is prob99 moot because few people will reach the FAA checkride standard in less than 15hrs pre-checkride with an FAA CFII. I took ~ 25 and this was done 100% in the USA.