Government-sponsored programmes always use graduate TPs (not just in fighter programmes, but in all programmes) for experimental work. I would suggest that use of non-graduates is the exception, rather than the other way round. Of course there have been some very eminent test pilots who have not attended a school, and smaller companies do make more use of non-graduate pilots, I suppose because they cannot afford the training.
The suggestion that a graduate test pilot with a high performance background would not know how to test a light aircraft is far from being a correct statement. I think on reflection you would probably like to re-word that one!