There was a pretty well covered case something like 15 yrs ago of someone massively obese that completely stopped eating and only consumed supplements to keep the bodys micro nutritions In order (which was continuously monitored by doctors). Iirc, he kept it up for 2 years until he got his target weight.

It's definitely a solid advice to keep to that rule of thumb though, albeit it'd say it's mostly a caloric delta you've gotta worry about: don't go beyond a sustained deficit of ~1k (consumed calories - used calories). It's fine too spike it occasionally in both directions, but going beyond will likely get you in trouble unless you're monitoring your health very closely