Yes, probably anyone can become a master painter, but for a person with a disposition and love to painting it's easier to start and to keep going. For someone who loathes painting, it's massively, prohibitively harder.

Success in any craft (and science) in 5% talent / luck and 90% hard work. But the love to the craft / science makes exerting this effort massively more rewarding. I don't think that training oneself to be a master is not attainable for someone who does not have a burning passion for this specific mastery. For instance, a mastery of programming might be a gateway to other things, for which the passion is burning.

The number of things for which ability to code is now a gateway is growing, be it financial modeling, computational chemistry, linguistics, etc.

Also, there's mastery and there is peak achievement. Everyone (except severely mentally disabled) can be taught writing skills and write nice, clean, well-organized texts. But probably not everyone can become Hemingway or Borges or Nabokov.

Equally, everyone can be taught to write nice, clean, well-organized code. But probably not everyone can be a superstar like Knuth or Norvig or Carmack.

So I'd reserve the word "talent" for the highest achievers. Talent is not required to be a decent programmer.