Lots of things claim to make people more productive. Lots of things make people believe they are more productive. Lots of things fail to provide evidence of increasing productivity.
This "just believe me" mentality normally comes from scams.
Why not? If you ever got an AI generated email or had to code-review anything vibecoded, you're going to be suspicious on who's "more productive". I've read reports and studies and it feels like the "more productive" people tend to be pushing more work onto people below or beside them to fix the generated mess.
I do believe there are productive ways to use this tech, but it does not seem like many people these days has the discipline to establish a proper workflow.
Naming another example outside of LLM skeptics asking it, about LLMs, is inherently a counterexample.