Not sure about the "like asbestos" for sure, but our bag has warnings about keeping away from pets, avoid inhalation, keep out of eyes, wash hands, etc. etc.

I put a link in another reply, dunno if you'd consider it credible or not, but I got it from a websearch for "inhaling diatomaceous earth" if you want to look at the many other links.

Food grade isn't as bad as non-food grade, but still not great. And the "aabestos-like" bit was in the context that it causes harm through a similar mechanism (small sharp, jagged particles). Severity and outcome might vary.

It's particularly bad for them but that doesn't mean it's perfectly safe otherwise. I wouldn't use it at all with cats or especially dogs, since they explore their world with their noses. A lot of the claims that it's safe for pets say something about if it's food grade, it's safe for pets to ingest the small amounts needed for pest control and then ignore how dogs get right up to things with their nose when they say "but don't inhale it!"

https://www.earthworkshealth.com/post/myths-and-misconceptions-about-diatomaceous-earth