There should be the seam allowances, the wadding and probably the chest canvas there; you would find that on most coats. So yep, more than three layers. But it does look like the bump is created by the seam allowances - or is there an extra piece of wadding with that particular shape too?
I'm actually asking out of curiosity and pure interest, not stating anything - it's you who owns the jacket after all, and I haven't seen NSM stuff in real life.
Someone should send JefferyD a NSM jacket.