To say "such a song to be inspired by tradtional songs and not by modern, commercial pop/rock" is really just another way of saying it has to be something "I" like.

Nope.

Spend a month listening to nothing but traditional folk music. Then spend a month listening to nothing but contemporary folk music. There are noticeable differences, which I'm not going to try to quantify since the gray areas are so huge.

Saying you're confused about the issue and then making a judgment that demonstrates a lack of knowledge doesn't sit very well. Perhaps you should get more educated before making a decision for yourself about what traditional folk music is.

WARNING --- WARNING --- WARNING
None of this has anything to do with what I like, or what anyone else likes. It doesn't in any way address issues of quality, importance, or relevance. It doesn't address what anyone should play. It's just saying that traditional music, for the most part, sounds different than modern music. It came to be through a different process and that process leaves its mark, whether or not anyone else can recognize it.

To me, a new song that is composed "in the tradition" should be created, both musically and lyrically, as the result of the composer's deep immersion in whatever tradition he or she is writing in (or by one who is very clever at picking up the essentials and reproducing them). Anyone who has listened to enough traditional folk can tell the difference.

Almost the most important thing is that the gray areas are huge and very subjective. But that doesn't mean that the lines aren't there somewhere.