Their overt position is that they want a bilateral FCL treaty with the USA. IMHO the USA will never sign such a treaty, in the current security climate. And why should they? They dish out 61.75 papers to anybody who wants them.
EASA pretends that "61.75" is beneath them; a full treaty is the only acceptable "European way".
It is however possible that EASA is trying to do a "Saddam Hussein extra mile to avoid war" job on this, i.e. they know the FAA will never go for it, so they can say "we did our best but the FAA did not play ball, so we had no choice...". These people are seasoned old foxes, as is obvious when you meet any of them.
I couldn't agree with you more, IO540.
I would also add that the real political agenda here, IMHO, stems from European airlines' desire to be granted greater access to the US market, which they hope will be granted under a blanket bi-lateral agreement. But as you state, IO540, in the current security paranoid climate, Uncle Sam is highly unlikely to allow the next generation of FAA licensed terrorists to be trained outside of the USA - they'd far rather train them themselves.