I'm sure Anthropic have too many applications submitted that are obviously AI generated, and I am sure what they mean by "non-AI-assisted communication", they don't want "slop" applications, that sounds like a LLM wrote it. They want some greater proof of human ability. I expect humans at Anthropic can tell what LLM model was used to rewrite (or polish) applications they get, but if they can't, a basic BERT classifier can (I've trained one for this task, it's not so hard).