I've also had an experience at YVR MLL where they scanned my BP, welcomed me in, then said "wait, can I see that again?" and then mentioned the SS.

I don't think it pops up a "please invite to SS". I think it pops up a "yes" and your PNR, and if they are knowledgeable enough and actually take the time to look, they can see "oh this is paid J intercontinental" or "oh this is Aeroplan Business Flexible intercontinental".

I wish it popped up a giant "please invite to SS" message. I remember one time flying YYZ-TLV or something with a friend (paid J), and he'd never been in that MLL so wanted to check it out. The agent who checked him in advised him he had SS access. The agent who checked me in did not. In that case it was fine because we knew we had access, and knew where it was. But I suspect YYZ has a lot of customers who just see "oh look there's the lounge" and go in without thinking. YVR at least only has the one entrance for both, but people still need to be informed, because not everyone knows that AC has two types of lounges.