Once you've interviewed a number FI(R)s for jobs, over several years, you kind of get used to them not knowing much about their privileges and restrictions. Of course, I've only talked to candidates from a little over half-a-dozen FIC providers, but that doesn't seem to feature very highly in the courses. Perhaps, they expect that kind of thing to be sorted out by their supervising FI?
I once had an instructor who'd done a dozen or two hours elsewhere, actually arrive with some supervised solos already on their form, including ex.14
which their previous supervising FI had allowed and signed-off on.
I find the definition of "first solo navigation flight" is always a good one to ask them.