"I can state flatly that heavier than air flying machines are impossible.
— Lord Kelvin, 1895"
I'm sure this doesn't apply to you since you're not Lord Kelvin. On the other hand, people like Peter Norvig state in a popular AI textbook that, for example, they don't know why similar concepts appear close by in the vector space, so maybe you just know something other people don't.
I'm not taking a position here but the person you're replying to stated that Anthropic are working on AGI, not that their current LLM offering will evolve into AGI.
False, and you've given no argument to the contrary. There's certainly no definition that precludes it. It isn't, currently; there's no reason it can't be, any more than there's reason that Conway's Game of Life can't be, given sufficiently interesting data to process. Any Turing-complete system could simulate AGI. It might not be the most efficient mechanism for doing so, but that's not the question at hand.