I can understand this, up to a point - though it does imply that the other singer would be "offended" by this, and why on earth should they, unless they feel some sort of competitiveness, beats me.

But it gets much worse. I have known of people being reprimanded for singing "someone else's" song even when the other singer is not present. And in some cases I have seen new arrivals at a club being "ticked off" for singing "X's song", even when they don't know "X" or his/her repertoire.

In other words, what starts as politeness (even misplaced one, in my view), ends up as a limiting practice which does not allow the "better" or "more popular" songs to spread, simply because someone else got to them first. So if a young/new floorsinger turns up, what chance do they have, if they have to check first who is in the club, what their likely repertoire is etc...That's why I think it gets silly.