we had a discussion like that before. figured it could be a loophole for a god under disguise to be invited in without the master's knowledge of their identity, and Athena might've been able to infriltate the hotel like that.
yes, that's the loophole. it doesn't explain the conditions in which the master invitation takes effect. so if via message or if the master must know who they are inviting are possible exploits. there's also direct contact, they could persuade the master in to taking them in, through a bargain of sorts, deception or even an honest request if the master doesn't see the harm in it.