I like the transition from “I have an issue with what you said” to “I have an issue with what I imagine you said” after getting clarification
That aside the statement was fine as written. For example it takes deliberate and active misunderstanding to twist the statement “people eat meat” into “there aren’t any vegetarians”
If there was really nothing wrong with the original phrasing about rich people, then there's also nothing wrong with GP's phrasing about poor people. The usages are exactly parallel.
Hang on, no, imagine if someone said "people eat meat" and it was the core part of an argument that people need a minimum of 2 acres of farmland to support their food consumption. It would be important to point out that vegetarians and vegans need less than an acre.
The context matters and blanket statements can be misleading in certain contexts.