Personally I think that was an "accident". They just wanted to put a Foreteller there to make it more mysterious, they didn't realize that some people could "hack" in the game and find out what character they used. Wich then turned out to be Invi, while they actually wanted us to believe it was one of the 5 Foretellers and that Foreteller would remain unkown.
Or they really had a storyline planned for him and just changed that over the course of time. Wich is actually kinda plausible I think. This game was first supposed to be non-canon, and now it's canon, so it's bound to have some changes in the script.
Or they just forgot. I really hope that's not the case though, but I don't see them making a story around Invi in a month dating all the way back to the first Anniversary event :/ (wait, how much time did pass in game?).
Also, Invi is a Foreteller, a Keyblade Master, of course he is going to investigate when 5 travelers from another world come into his world. He then saw that Player took care of the situation and decided not to interfere. Maybe at that time the 5 Foretellers still even worked together and they unanimous decided that Invi should investigate.
Wich reminds me, what happend to that cloaked guy in one of the first CoL events? He still isn't confirmed either right? (we gonna look at that zipper and decide whether it's MoM or Luxu?)