For the longest time I thought one can invite a chat user to the site's main chat room if and only if that user has used the site's main room recently. But it turns out, simply being in whatever room activates the option (first two screenshots are unedited apart from arrows):
What I see when I'm *not* in a room:
What I see when I'm in a room:
Proposed change for when the inviter is not in a room:
The proposed change will make it clearer that it depends on the inviter, and not the user being invited. (In my case, I realized that yesterday, after +5 years.)
From a comment: another possible wording: "You aren't in any rooms this user isn't in." Perhaps with a link to a help page that explains the conditions in detail: "A) you are in that room, B) the prospective invitee is not in that room, and C) the prospective invitee must have access to that room."