An eating establishment has always been seen as public property for the purpose of many laws, but in any event, they had no personal expectation of privacy in the eating establishment. The police were there for the express purpose of responding to a citizen call alledging a crime took place, something you're very carefully dancing around. In the course of the investigation, they asked for identification.
If this was a case of cops just walking in for dinner, seeing patrons and demanding ID, then I would agree with you. That wasn't the case.