Positive.
And yeah, that's happened to me a lot, too. Sometimes I'll only get, say, someone's Street Fighter or nintendogs StreetPass, but not their Mii in StreetPass Mii Plaza. I believe this is because each title that transmits StreetPass data does so separately, so if the connection is somehow interrupted during StreetPass data exchange, you may end up missing some StreetPass data. That's just my speculation, though. I've also encountered a few other weird things, like people getting my Mii through StreetPass Mii Plaza but I wouldn't get theirs.
And the invite thing is from Miis that aren't obtained directly through StreetPass Mii Plaza, but through other StreetPass titles. So, say someone plays nintendogs + cats using a Mii that's different from their StreetPass Mii Plaza Mii. If you StreetPass that person, you'll get both Miis, with the one from nintendogs + cats appearing in your Mii Plaza through invitation.