Maybe Shane was making the same kind of distinction between "Christmas Songs" and songs about Christmas that we might make about a distinction between songs like Home Lads Home and The Green Fields of France which are obviously about the War and War Songs. Would we call Christmas in the Trenches either a War Song or a Christmas Song? Anyway both songs are songs best sung around Christmas to bring out their meaning.

Of course there are songs that weren't at all about Christmas which have become Christmas songs by virtue of how people regard them, for example Jingle Bells which was a Thanksgiving Song. The opinions of the people who wrote or performed them are totally irrelevant. As is generally the case - songs are free agents, nobody owns a song except in a financial way.