Liz and I do beginners voice workshops at quite a few festivals and we get a lot of people who believe they can't sing because someone told them so, frequently when they were very young. Some of them have never opened their mouths since. By the end of the workshop we have them singing in unison quite happil;y and in tune.
We once had a lady who was slightly below the pitch [clinging to the lower end of the register :-)] and when I asked her if she had had a hearing test done recently she told me she was fairly deaf. She was accurately reproducing what she could hear but was only hearing the lower frequencies in the harmonic.