I signed a release when the employer did a background check on me. And was provided a copy of it. The latter I think is state law here, the former I think is also law but I’m not 100% sure.
I can believe it's a state law--or even a company just doing it as a matter of CYA policy. I assume it's pretty easy to run a background check without someone knowing though. And of course it's quite common to provide reference although I don't know how commonly companies contact them--I suspect not often.