On the other hand reproducing the tone requires practice, and mostly practice with your vocal instrument.
I would imagine that kids who grow up in families where e.g. mother sings while cooking, don't even notice how they practice at the age of 2 or so. But what is important, they train their voice, not only hearing.
It is like with colors. A person can see colors perfectly, but if you asked to mix acrylic paint to get chartreuse? Most of the population would struggle I would believe. We wouldn't call these people color-blind.
However with music I feel we somehow mix tone-deafness and ability to sing/reproduce tone.
Mind-bogglingly one can apparently be tone-deaf and still be able to sing in tune.
On the other hand a person lacking ability to tell green from red can still paint quite good landscapes?
I find this hard to believe. Human voice has a lot of timbral characteristics that show up on a spectrogram view. It would also imply that a person would be unable to tell the difference between a piano, a guitar and a trombone. This would also make understanding speech very difficult. Do people (with otherwise normal hearing) like this exist?
This is pretty different from not being able to distinguish musical pitch, say tell C# from Bb, or be able to tell which one of the pitches is higher.
It's no surprise that I didn't make any real progress, since I wasn't learning an instrument and my school teachers made us sing but didn't bother trying to teach us to sing -- but by late primary school I was a notably bad singer relative to (almost literally) everyone else in my class. My home was by no means full of music, but we did have a record player and my sister liked to sing with my mother sometimes. And although it took me a while to get interested in pop music, by late primary school I had a CD player and some bands that I liked.
So I doubt the difference in ability was solely environmental rather than innate; surely the other kids hadn't all been taught how to sing, or grown up in very musical households. (I'm still very weak musically, and still can't sing, but I'm not literally tone deaf.)
My wife and I listen to a lot of classical and hymns with simple 4-part harmonies. We have 7 kids, most of whom could match the songs pretty well at surprisingly young ages (2 or 3 years old).
What makes you think that’s not nurturing?