Just because traditional and copyright tunes are played cheek-by-jowl at sessions doesn't mean that people aren't aware of the difference. I think, for example, that most musicians sitting in a pub would be aware that Yesterday and the Foxhunters Jig are different sort of animals. The grey area is the modern tune composed in the trad manner. Some people would know Da Slockit Leet is a recent tune, and would know who wrote it. Others would maybe know the name of it, but not its provenance. Others would know the tune, but not its name or origin or anything
Doubtless this is because writing a jig or a reel in the traditional manner is a skill easily mastered, any fool can do it. Writng a song that can pass for traditional with an experienced folkie: now, that is a very very difficult art indeed!