You are arguing an ideal and they are making a point about practice and fact. The practice on the ground and public policy is that certain "public toilets" are for the homeless. This informs government decisions about how they are designed, who has to maintain them, where they are placed, and who uses them.

A public toilet in the tenderloin is a homeless toilet in all but name. A public toilet in Golden Gate Park is actually a public toilet in the sense that you are talking about.