That's what I told my kids. They weren't allowed to use Wikipedia either, so I told them to use it for the sources referenced there.

Google Search content farm results should not be allowed, but good searching might turn up some decent material so I think it should be taught but with those caveats. Is it too much to ask that the teachers at least give a cursory review of the source links students submit, and give feedback to the students who are not choosing good ones?

Back in my day we were allowed to use popular magazine articles as sources (Time, Newsweek, etc) and honestly those probably weren't that great either (see Gell-Mann amnesia effect).