As far as I know, there is no longer any problem with mixing and matching licenses, exams and ratings from different JAR states
There is no indication on either the JAA or CAA websites that anything has changed in relation to the 'State of Licence Issue'. Both JAR-FCL 1 (Amendment 3) and LASORS 2004 say essentially the same thing -
"An applicant shall demonstrate the satisfactory completion of all requirements for licence issue to the Authority of the ‘State of licence issue. In circumstances agreed by both Authorities, an applicant who has commenced training under the responsibility of one Authority may be permitted to complete the requirements under the responsibility of the other Authority."
Note the phrases "In circumstances agreed by both Authorities" and may be permitted to complete". This means that you could start your training under one National Authority and then, provided that both Authorities agree, you
may be able to complete under a different one. However, this does not mean that you can chop and change at will.
If you wish to complete distance learning in the US, then your 'State of Licence Issue' will initially be whichever has approved the course that you wish to follow and you would have to take the examinations set by that state. In the case of courses approved by the UK CAA, it is possible to sit the exams in the US, in all other cases you would have to travel to the appropriate country to sit their exams.
Should you subsequently wish to carry out the flight training at a FTO approved by a different JAA Member State, you would have to obtain the agreement of both National Authorities to transfer and the new 'State of Licence Issue' would be the one (not surprisingly) to eventually issue the licence.