I find it strains believability. Mileage will vary for others, but for me the exact same uniform without variation doesn't say Kelvin uniform. It says to me that the simplest explanation is a temporal soldier served in a time were that uniform was used.I am hypothesizing based on presented evidence (what was said).
So, what, the Prime timeline can 'spawn' the Kelvin Timeline, but the K.T. can't have same uniform and combadge from the Prime timeline and about 13 years after the said uniform and combadge were seen in the Prime timeline?
Is there some kind of unwritten rule that says the Kelvin Timeline MUST be completely different from the Prime Timeline and that there is 0 room for the possibility the timelines could have actually 'aligned' somewhat the further away from the Narada's incursion point we get even though we have evidence from Trek itself which demonstrates that even if you do change one thing, certain things would still unfold in exactly the same or similar capacity?
Regardless of the possibility, I didn't for one moment believe that Prodigy occurred in the Kelvin universe. To me that's an assumption to excuse away lack of preference of the ship design elements.