Guys, I think that the reason Nitori is in 13.5 is because Tasfro couldn't put her in 12.3 due to lack of time, so they're making up for lost potential by putting her in this one.
Also, if one recalls that there can be mirror matches in the games, then it can be suspected that the "character in background = not playable" theory is false, if only for that reason.
Hell, gods like Kanako and Suwako can divide themselves infinitely in canon, so Tasfro don't need to alter squat for who's in the background.
Basically, my thought is this:
If Reimu vs. Reimu is possible, then it's possible for playable character to be a background character at the same time. I can imagine a Reimu vs. Reimu match at Hakurei Shrine, with a Reimu in the background either watching the match, or being annoyed with everyone else. In other words, if there can be two Reimus, why not three?