My wife and I encountered this some years ago. Also a volunteer situation for us, this was a college jazz performance class which we assisted as staff for a number of years.
This particular student singer actually had remarkable stage presence, but he had no ability and no interest in counting or keeping the tempo or rhythm. He was a nice enough older gent, and he had pretty nice Sinatra-style voice quality, but he bristled whenever we suggested counting -- "I've never had to count before, this must be your problem" was frequently his response -- some backup people had obviously spoiled him in the past.
He was nearly the end of the combo, all the students feared on-stage work with him because he was totally unpredictable. There was no option with him except to stumble along and change the rhythm and tempo as needed to suit him. It was probably good training for the other student combo members, but it was sort of a shame to have to put them through it. Happily other singers -- who could count -- regularly floated into the combo.
That isn't to say that other combo vocalists and instrumentalists didn't also have various problems, and it's not like we haven't encountered other similar vocalist situations since then, but this was the most memorable situation. It was pretty horrible, we still occasionally talk about him, some 10 years later.