Great photos and post - I think you are right and your wager is safe. I think youve proven beyond doubt that this is indeed the source garment
The reference to it being 'British' may be an interview innaccuracy or it may have been issued to British forces.
I am assuming Nigel knew the origin was the US as he has done a garment called 'US navy clip jacket' which is a jersey hooded top with these fastenings.
Interestingly I've just looked in Nigel's 'Ascent of Cabourn' book from the 2003 collection and the clips used on the first photo of the Cameraman are exactly as the US smock and there is a page featuring this clip describing as a 'naval clip with rivets'
The garments photo'd in the book were samples which were made to look worn and I do know there were modifications made on some garments when they were first released so was there a Cameraman first released which had the same clips or was the 'ladder' type adjuster specially designed for this jacket from its first release?
I now think that the ladder type adjuster is a NC design but can't be sure - need more research