Maybe it's semantics, but I don't agree with what you are saying
gibr monkey
Whether or not a FAA or foreign medical is required, has nothing to do with if you are flying for training or not, but it has to do with the certificate you are using to be able to fly.
If you are coming over to the US to do a JAR-nightqualification, one of the requirements is to fly solo at night. Since you don't hold a nightqualification yet, you cannot fly based on your foreign license. Therefor you need to get a student pilot certificate, and the proper endorsements. Since now you are not flying on the foreign certificate anymore but on a US certificate, you need a FAA medical 3rd class or higher.
For training for a CPL as long as done by day, or dual at night, or solo at night when in posession of a nightqualification on the foreign certificate, you can fly on basis of your foreign certificate, and your foreign medical. However for the actual FAA CPL test, you will need a US medical, since it is
one of the requirements for taking the test. If you are coming to the US to do a JAR-CPL course/exam, a US medical is not required.
As long as flying while respecting the limitations of both FAA
AND foreign certificate, a foreign medical is sufficient.