I'm surprised you haven't offered up a one armed bass player or a man in a long term coma.You readily offer a definition of zero skills for singing, which is kind of harsh, but a person who "can't even hear that they aren't making the right notes" would have no inhibitions about singing and thus sing with all atonal glory, simply because he desires to sing, and catch the attention of a woman who has the same musical disability. By your own standards, you cannot refute this claim because you need to have seen evidence that everyone cannot do it, or you've seen such a wide cross-section of backgrounds and aptitudes from wunderkind to dunce to confidently say 'no one' can do it.
You're coming at this from a standpoint that all roadblocks are in the mind.
With vision we have figured out that a lot of people have impaired color vision. No amount of effort can overcome this. Why do you not understand that there are almost certainly many other impairments that haven't been decoded sufficiently to prove they are physical in nature rather than simply having no color sense.
This thread is about men who believe themselves to be not attractive to women. This includes various beliefs that oneself cannot overcome perceived inabilities and deficiencies.
Belief and perception, by definition are a phenomena of the mind.
For myself, I've never learned to play a musical instrument or have ever amassed any great amount of money. In spite of that, for the past fifty one years, I've been in a series of sexual relationships with women, with very short intervals between one and the next, with some overlap. Of course, I believe this can be attributed to being a poet.