For a JAA FI to be exercising the privileges in the USA he would have to be working within a JAA approved FTO. One of the requirements of the approval is that the FTO must have a detailed Operations Manual which includes details of all aspects of the supervision required.
Also what if the student does not have a CAA ref. no.? do you leave the boxes empty?
It is not uncommon for a PPL student in the UK not to have a Reference number; if they don't have one, you can't include it.