They do not allow IR training in the US, they only recognize IR training taken place in European Airspace.
Incorrect.
You can complete part of your training in the US. I know one school which does 25 hours single, 5 hours multi then 10 hours sim, 10 hours multi in the UK. A lot more aircraft and real IR time than some courses in the UK.
Some training may be completed in the US just not all.