The negative proof is there in the definition itself. Transformers are not AGI, they're frozen human intelligence of the autocomplete variety. That can never be AGI and anyone who says otherwise doesn't understand transformers or AGI.
So yes, the LLMs can be trivialized as just randomized autocomplete, but if you add a database or memory to the side very basic MLPs can become a Turing machine. It's going to take a lot more proof to say a Turing machine could never be intelligent. And you can do more than just give the LLM side memory - you can have them invoked recursively, use message passing as coroutines, and so on...
You might be technically correct if you ignore anything other than the very restrictive definitions you're using, but even there I'm not certain. If you had a LLM with a trillion token window, is that good enough to act as a memory? Human brains aren't infinite either.
However, I've got a 20GB GGUF file on my disk that can write code better than 99% of the people I ever worked with in the last 25 years, and ravens seem pretty clever with about 2 billion neurons... I have no idea what the lower bound is.
Fun to think about though :-)