The headlining is a non structural component. It was simply a choice to use that rather than a more conventional foam on ply lining or foam on fibreglass lining.
Personally I think it was a good choice, it is very easy to clean and keeps the boat looking tidy with the minimum of maintenance, although I'd prefer it if they had put more thought into access behind the moulding for rewiring and stanchion base repair.
Whether or not the Trapper deck has a full balsa core or not, which I doubt, the headlining is irrelevant.
If there is a core, I imagine it is only in the flat sections of deck, and I don't see the point of doing it with spacers.