I have always believed that tone deafness is a physical ability and not particularly common.
The inability to sing accurately appears to come from a singer not being able to listen to the sound they are making and relating it to the physical act of voice production. It seems to be a fact that some people have to work harder than others to sing accurately, but this is a matter of concentration rather than physical ability.
The traditional trick of cupping the hand over the ear, though usually associated with folkies, has been used for centuries - maybe millenia - as a device for listening to the voice and producing accurate notes.
Jim Carroll