In Summer Knight, Harry doesn't enter Murphy's house until he is explicitly invited and even then he feels the tug as he enters, leaving some of his power at the door. It makes him uncomfortable.
In all the iterations of this concept it seems like the person has to express an actual invite, even if it's just causal conversation. It's like the vampire shows up at your door and you don't know he's a vampire. You chit-chat in the doorway for a bit before realizing your manners have slipped and blurt out, "Come on in. I'll make some coffee." Stuff like that.
I get suspicious of people who say things like: "Aren't you going to invite me in?" or "If we can go inside, I can tell/show you more..." Things like that. It's like what are you getting at? Why do you want to come inside?
In mundane areas... it's like police can't enter your home without warrant, but if you invite them in, it's the same as if they had warrant, you know?
Also, the permission to enter can be implied if the supernatural beastie says, "Can I come in?" And you simply nod or step aside to grant them entry. That's like an implied explicitness (an oxymoron, I know!), but you know what I mean? Had the supernatural not asked, then the context would be different and it would not be an invitation. Like, I stand aside and the beastie just stands there staring at me until I say, "Well? Aren't you going to come in?" And then, you see, it becomes and invite.