I only have anecdotal plus a bit of thinking...? Talent is pursued interest; genius is pursued passion. Most people won't have passion for mathematics, even if such passions were heartily encouraged - at the very least, because there are so many other things to also be passionate about.
I can get behind that, if we defined genius to be pursued passion. Not everyone has a passion for mathematics, that is true.
I just thought what the root post was implying is that even if you're passionate, you might not have the potential to achieve genius-level skill because that would somehow be genetically predetermined. If that was what he was implying, I'd love to see some evidence to support the claim.
I feel as if it is also somewhat true in that regard. I have been extremely passionate about music for more than half my life yet I am still horrible. I believe the same applies with many other skills in life.
Any and all skills? No. Mathematical and other related intellectual skills? Why, yes, I do. Despite what most people say, I've never seen a genius who hasn't worked at least twice or thrice as hard as his peers. I've never seen a child that, without the help of any tutors at an early age, or without any influence from their parents, was simply spitting out non-trivial theorems from an early age. I have a hard time believing that some people are BORN better at math and logic than others, and I've yet to see any evidence to suggest that.
Quite on the contrary, I've seen plenty of evidence to suggest that genius is at all not genetic, and that you can train children to become prodigies, and later, geniuses. Surely you've heard of Judit Polgár, universally considered the best female chess player of all time? She was made a genius, not born. Her two sisters grown to become Grandmasters as well. And here's Dr. Frankenstein: https://en.wikipedia.org/wiki/László_Polgár
Not everyone who wants to be a math genius is. Desire is not sufficient for mathematical aptitude, and I'm not sure how you can honestly define potential to yield a case where both potential and desire can exist without achievement.
But to be a genius, you don't have to be the best, only one of the best.
The article also never claims that everyone IS a mathematical genius, only that they have the potential to become geniuses. Whether or not the achieve this potential in their lifetimes is another matter entirely that doesn't contradict what your quote implies (that only a small percent of the population can be among the "best" at any given time, by definition).