Oh, they had the proofs, thanks the lack of ability by japanese writers and screenwriter, Shirley blood mucked up Lelouch shoes, then footprints, etc..then the presence of other people was a confirm.
The blood can to give a lot of info if a detective investigate it.
Lelouch and Rolo escaped without the time to clean or move evidences, then....shirley made suicide thanks the universal motivation "because yes!"
Otherwise....
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