Agreed. The innate gifts are a matter of natural talent. There are people with talent and training, there are people with talent and no training, and there are people with training and no talent (who have learned the physical mechanics of playing an instrument but can't do the things that come naturally to innate musicians). Those in the remaining category (possessing neither talent nor training) tend not to play in public, so they're less in evidence; though we've all come across them at one time or another - usually at the least convenient moment.

Therefore the equation is slightly skewed. But true musicality - like being good at numbers or ballet or sports - is something you either have or you don't. Training will not give it to you if it's not there to begin with (as I know from decades of being a music teacher). But classical study can develop and enhance one's natural gifts, and it does not mean the death knell for improvising, playing by ear, harmonising, etc. Lack of talent does that.