I think that is at least in part because for a few years, every time someone thought they had a RESTful system, some genius would come through and declare it non-RESTful on account of not following some rule or other. So "RESTful" came to mean a type of HTTP API that tends to look a certain way. And so of course URLs matter.

Saying something is "RESTful" is a surefire way to find out the ways in which it fails to match up with what some obscure document says.