Hrmm....... Yeah, that sounds plausible enough. Taking that back to the beginning, we've got:
---> Chihiro almost certainly trained with someone. (If not, how could the murderer have known where she was? Sakura's testimony corroborates this anyway.)
---> Chihiro is almost certainly a man (ample foreshadowing + coffee stain/posters indicating that the crime took place in the male changing room).
From there on, we can deduce that her training partner is pretty much confirmed to be the murderer. Chi's body was found in the female changing room - however, his training partners should know by now that Chi is a man - and that his murderer must be a man also. However, shutting up means that a female is likely to be suspected, which means everyone dies. Therefore, only the murderer would have a motive to shut up. Building on that, we've got two conflicting theories:
---> Togami was Chi's training partner; he killed him, then doctored the scene to frame Fukawa.
---> Not-Togami (a man) killed Chi.
If we assume Togami is the murderer, we quickly reach a dead-end. Chi would have to be an absolute moron to choose Togami as a partner, knowing that the guy openly stated he aimed to kill someone and graduate (this might not have been what he truly meant, but the cast interpreted it that way, and that's all that matters). Furthermore, Togami would have to be an incredible idiot to mess up Syo's MO that bad with his life on the line... and then proceed to show Naegi all the evidence against him. Also, what kind of an idiot culprit would use the extension cord as a rope?
Sure, he's arrogant, but he's not that much of an airhead. Moreover, orenronen said that Chap 2 was his favourite chapter. Togami being the murderer would leave this chapter without a real plot twist, and I don't really see why orenronen would have liked it that much.
If we assume Not-Togami to be the acceptable solution, we've got two possible alternatives for the murder:
---> Culprit kills Chi. Switches the scenes around to shift the blame on the girls. Togami comes in, assumes Fukawa to be the murderer, doctors the scene to make it look like Syo did it, and then proceeds to inform Naegi in order to make the framing/accusing easier. Since he's sure Fukawa killed Chi - and since he knows he himself isn't the culprit - he's not as thorough in his doctoring, making small mistakes like the use of the extension cord. He really thinks he's playing smart by making sure the true culprit takes the fall. This hypothesis means the true culprit is passably smart, and Togami's an idiot (but nothing too bad).
---> Culprit kills Chi. Doesn't switch the scenes around and just leaves the room (he's in panic, doesn't know about the letterbox and just doesn't want to be caught). Togami comes in, sees the scene and decides to do a little switcheroo, all the while framing Syo. He does that to gauge reactions and entice the true murderer in slipping up by saying something he couldn't possibly know. Perhaps he's trying to see who's most likely to jump on the Fukawa-Syo bandwagon. Perhaps he has a further trap planned. Who knows. This theory means the true culprit is somewhat stupid and Togami's a magnificent bastard. I think it's somewhat less likely than the first alternative, though, if only because I think only Kirigiri and perhaps Celes are smart enough to try such a plan. I don't think Togami has it in him.
The training partner has to be either Mondo, Ishimaru or Hagakure. Of these three, Mondo is the most likely culprit, for all the above reasons. The card especially strikes me as very interesting - Monobear pretty much confirms that it's not Leon's. So either it's Chi's broken card or Mondo's (through steam/sauna - Mondo didn't take off his clothes, after all).
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When you have nothing to say, quote yourself ~ Solfadore