I think the claim is interesting, and I certainly wouldn't reject it. But just relaying someone else's claim, without any substantiating argument, I find quite uninteresting.
Jean Philippe Aumasson[1] is an important currently active cryptographer who studied this particular problem closely. If he says he does not expect an algorithmic break of SHA2, I believe him that I don't need to plan to switch from SHA2 to SHA3 in an hurry.
I don't have the math to understand a more detailed explanation for his reasons to make such a statement. If you do have the math, ask him.
