How would you go about demonstrating that this assertion is true? Is there some kind of test that could be performed?
For what it is worth, I disagree (at least in part). I think most skills can be trained, and most skills can be improved. I suspect most people have some kind of minimal natural photographic eye that can be trained. if they didn't, there would not be an audience for photography, as no one could tell good from bad.
The part where I agree, is epitomised by the fact that my cat cannot take an exam in mathematics or art, and no amount of training would make any difference to this. Clearly at the extremes, there must be at least some kind of genetic component present. But people aren't cats and perhaps we all possess some talent, some "eye" that can be trained.
What doesn't seem possible is to be able to tease this out talent from training just from looking at the photographs. Is this photograph the product of raw talent or some talent plus extensive training? It seems to be quite natural for viewers to ignore the presence of a trained element and jump to the assumption it is all down to talent. But we know people like to hide the training and present the talent. The waste bin is a photographer's best friend. How could the viewer ever know?
I don't consider myself to be a creative person - at least there hasn't been much evidence of it in the past. I can't draw, I can't play music, I can't dance, I can't write plot lines, I can't sing, I can't paint, I was always the one in team meetings terrified the finger would point at me and the question posed "David, what do you think we should do to solve the problem?"... yet, with photography the mechanical element has released me from some personal limitations. I seem to have been able to develop a concept of what makes a decent photo (at least ones I like) and to glean some idea of how to put that knowledge to good effect in making my own photos. And although the absence of original thought still seems to be present in my photography, I can at least bend a scene towards the kind of photograph I like. And my awareness of the negative elements that ruin a photo has improved, as has my ability to excise some of those elements from my images. I feel as if my current photographic "eye" far exceeds where I started from. And that doesn't feel like the result of talent to me, but of training. I have found the very best training is looking at lots of photos and intuiting the ones I like from the "buzz" of adrenaline. Then I take the elements of the "buzz" photos and build them into my images. And the better ones provide at least a frisson of that "buzz".
I feel that constitutes evidence that training is more important than talent. But an actual test of some kind would be useful.