Crowhugger, my friend was not always so much off pitch as just singing the wrong notes - e.g., notes that were neither the melody nor a reasonable harmony. It did seem sometimes like he just couldn't grasp what the melody actually was or what notes would harmonize with it. But what was so odd about this was that he could do this just fine playing a fretless instrument, so it obviously could not be anything resembling "tone deafness."    He just couldn't make his singing voice do what his stand up bass (or his guitar) could do. it was as though he could "hear" notes and intervals in instrumentals but not in vocals - at least not his own.
I have no doubt he could have overcome this with time and practice, but he gave up on it fairly soon and just stuck to instrumentals for the jam sessions.

I don't know if it's relevant, but he did, unfortunately, die of brain cancer a year or so later.   I don't know if there is some part of the brain that would affect pitch discrimination in self-produced vocals but not other people's vocals or in instrumental music.