While I agree that people can be trained, the diversity of ability can be seen in my family - all having the same start and my Mum singing the same sort of songs to all of us.
I sing in tune, prefer to sing harmonies and play almost any instrument I can get my hands on.
My next sister enjoys singing, especially hymns and Christmas carols, but usually she's singing in parallel 4ths or 5ths and doesn't know it.
The third girl can sing in tune but if I try to harmonise, she loses it - can't hold a tune against a harmony.
Number 4 is better at holding a tune when I harmonise, but she can't do the harmony herself.
Number 5 just doesn't sing. He used to as a kid but for some reason he stopped (maybe he had a discouraging teacher).
And the baby of the family is a musical genius! He was playing our pianola, with feeling, soon after he could walk. Our Grandmother taught him some simple tunes and at 6, I tried to get him lessons at the local convent. The sister said he was too young but he demonstrated his tunes and sang to her - and she started him the next week. He had perfect pitch and could name any note you played him. He's now in his 40s and is a professional musician, musical director, accompanist, and teacher/trainer of singers. He has a teenage son who also has perfect pitch and a daughter who doesn't (though she is musical and could be taught).
So the nature/nurture argument could be tested on our family.
Oh, and my Dad was tone deaf! Everyone knew that! But Mum could sing and she did so frequently - singing along to songs on the radio, at church, in the car, anything could set her off and I tend to do that too.
Robyn