We have Silver status with BA = Sapphire Oneworld

Certainly if the lounge is BA owned and operated they will find you in the system and let you in. The problem is with non BA lounges - especially the independent chains. They have no way to check your status apart from your boarding pass.

I'm sure the same is true for other airlines.

If you want to bring in a guest, your boarding pass is not enough. In Madrid I had to log in on my laptop to demonstrate I really was silver status.