You can train and obtain an FAA license anywhere in the world as long as you can find
A) An FAA certified instructor (to sign you off)
B) A testing center to do your written exams (can be found world wide)
c) An examiner (DPE) who is approved by the FAA to examin in that particular district.
Ie. as far as the FAA view it Europe is one district covered by the New York ISO (International Standards Office....equivalent of a FISDO in the US). Examiners are only allowed to examin within their district - you can find FAA examiners at
http://av-info.faa.gov/DesigneeSearch.asp
Unfortunately that won't do you any good unless you allready have an FAA instructor on hand to sign you off with the appropriate endorsements required to take the practical test.
It is correct that the license can only be issed by the FAA in the United States - but the examiner will issue you a temp. airman certificate and mail the paperwork off to the states. Then the FAA will mail you back a fresh, green, plastic license within 120 days.
Good luck!
