Correct Irish_Stu,
It is possible for someone to be trained in their aircraft at a RF or an FTO. So that isn't too much of an issue. There are plenty of aircraft owners whom have been trained in their own aircraft. As I mentioned before training in a syndicate aircraft you will probabaly find insurance will be a problem. Alot of syndicates will require a 100 hours total time; alot will accept a fresh ppl but may then require an excess to be paid on the insurance; now you start discussing training in a syndicate aircraft then you can start seeing some complex insurance paperwork issues. Also are other members of the syndicate going to be happy about the aircraft being used for training.
Before EASA took over certification you also had the issue of private and public transport certificates of airworthiness; that is most private or syndicate aircraft were on a private C of A and for training you would require a public transport C of A. I am sure with EASA there was some rule change relating to the C of As but I can't rememebr the exact details.