I have to agree with Midchuck, and those who've expressed a similar viewpoint. If the song is out there, especially if it's traditional and/or public domain, the pleasure of performing it belongs to no one person. I do believe that credit should be given to the author of the song, always, if one has that information, but just because one person has worked on learning it doesn't make it exclusively theirs to perform.

In a song circle situation, common courtesy might suggest that certain songs be left for those who perform them regularly, but I would attribute that to consideration on the part of the others in attendance, rather than an unwritten rule implying performance rights. To deliberately perform a song or set that is commonly known to be a main staple of another's reperatoire, particularly if it is a limited reperatoire, is, IMHO, discourteous and mean-spirited, and goes against the spirit of music. It's not about competition, but about the sharing of the music.

As one who has done some songwriting and performing, I feel that if I have been "given" a song to write and record, and put it out there, then in a sense, it "belongs" to the world, and if it's enjoyed by others who perform it, well and good. But again, the author should always be acknowledged and paid royalties when others choose to record their work.