That's still quite a stretch to assume that. Considering...
1) The body was in the males' changing room.
2) The body wasn't killed with the trademark scissors.
3) The body wasn't crucified.
4) Bloodstain fever wasn't written on the wall.
Togami would have to be a complete idiot to think that Syo killed Chihiro.
There's also the whole thing about Mondo not knowing that Chihiro was out at night in the first place.
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maybe, lol