In practice . . if you trust your friends there's no problem up to that point. Once you go beyond that you need to be careful. Especially if you're charging for the material (I don't think it makes any difference in law, but it does tend to attract more attention).
My guess is that the Fiddler's Fake Book may well claim that their tunes are their arrangements and so are subject to copyright.
I assume you have an ABC tune finder index. See if you can find two or more sources for your tune - if so, and provided they don't all agree on a (C) source, you've good evidence of it being either trad or PD.
All IMO and I'm not a lawyer, of course!