This is all a bit stream of consciousness... hope I didn't drift too far from the plot ;-)
People who sing out of tune rarely sing consistently out of tune.
People who really cannot sing tend also to not be able to identify correct pitches at all - to greater or lesser degree. They're not fighting an inner tuning, they just don't have one.
The ability to recognise pitch is like most things natural, a bell-curve of population against ability.
Very very few people have zero ability to recognise or reproduce pitch.
Most people can kind of carry a tune, even if only in a bucket ;).
Again, few people have the ability to absolutely lock to a pitch with no external reference, known as 'perfect pitch'.
I can sing. I know I can sing.
I also know I don't have perfect pitch.
I have reasonable relative pitch, which is the ability to keep a tune up once you've been given the first note or a reference chord.
What I do have, once given that reference, is a very tight tolerance for being able to stick to it - so long as the reference chords continue. At that point, I'm in my element... constant external reference to which I can accurately nail a tune.
At that point, I find anything which is not in tune to be painful to hear.
Remove my reference, though, & I will eventually drift away from the original pitch. I'm OK so long as I don't hear any other reference. I can stay on pitch for an entire song, so long as I know it well enough, but I can be immediately thrown if I hear another tune, or another pitch reference of any type which doesn't fit what I currently have as my remembered reference.
Neural nets, or even regular computers, have a great advantage over humans. They have 'perfect pitch'. They can be taught to recognise what a pitch is by actually counting the frequency of a sound wave & just looking it up in a table.
Humans can't count that fast, nor do they have any kind of quartz watch type of reference to count against.
So, a human has to recognise a pitch & then reproduce it by 'natural talent'. Some can do it, some can't, to varying degrees.
edit of edit, though I'll leave the original gripe below...
Further research tells me this is probably not auto-tune. They just picked the chorus he did the best & flew it in down the length of the track - a fairly standard practise since at least the 80s, though usually just for the big, difficult stuff like huge block BVs.
It's still painfully sharp.
This song has bothered me for years & still hurts every time I hear it.
Specific ref is the chorus, first heard at 1:42 but I'm not going to time-stamp it in the link because you need to hear the entire thing to get the base pitching nailed in your head first.
The vocal is generally pretty tuneless, but the chorus [in fact, most of the 'money notes'] has been auto-tuned... by someone who wasn't all that sensitive to the song's base pitch.
The result is that if you sing along to it you need to intentionally squeeze your vocal about 5 cents sharp, each & every chorus, to hit what auto-tune pushed his vocal to, rather than what you would sing if left to your own inner reference.
It gets even more noticeable in the later choruses, when whoever is doing the BVs is actually closer to pitch than the lead vox.
I'm aware most people don't [can't] hear this - but it would be nice if someone did...