That's not right.

Your carrier will grant access to whatever lounges they want, usually it'll be their business class lounges except in unusual cases like upgrade certificates or last minute upgrades. Sometimes that carrier won't have a lounge and they'll have a contract lounge or another non-*A lounge they give you access to. Sometimes they won't have anything at all.

But in addition to that flying business class on any Star Alliance carrier grants you access to any other Star Alliance business class lounge in the airport you can get to.

And they might not tell you about this as they'll just tell you about their own lounge which might be cheaper for them. For example in SFO flying UA in business class they'll only tell you about their own business class lounge, not the SQ SK lounge. (though SQ might be closing access to this lounge now) Most airports won't have multiple *A lounges to choose from. Only large hubs like Heathrow or unusual cases like SFO would fall into this category.