I've run into a couple of people in the past like that. While, the problem is most often singing flat (due to incorrect support and posture) I have actually run into a person who consistently sings sharp -- just enough to be a problem (about a quarter tone). If you were to hear them with an instrument, they would sound fine, but they don't seem to make the connection with the keyboard pitch (even a perfectly tuned one). What's more, they will do it regardless of the key they are in. I suspect if one were to match their pitch by raising the tuning of a digital piano slightly, they would sing sharp above that.
I was accompanying for a college professor who taught privately in his home on Saturdays. He told me that it is nearly impossible to get a sharp singer down to pitch. Flat singing is usually correctable, but he had not yet found much success in correcting the problem with a sharp singer.
Anyway, I'm curious to know what they are hearing in their head. Somehow, what they are hearing has to be correct to them in relation to the piano. And, they can't be truly tone deaf since the notes are recognizable.
Oh well, such is the life of an accompanist.