I think that providing different liveries would provide notice to passengers that the line is either under different ownership or a different operator.
In Vancouver, the Canada Line has a different livery than the rest of the SkyTrain system. Although TransLink owns the stations, tunnels and the guideway, the vehicles are owned by the InTransitBC (the operator).
In the case of the Crosstown, if the vehicles are owned by MetroLinx, MetroLinx could allow TTC to paint the cars red to identify the operator - but as owner, if I were MetroLinx, I would require TTC to bear the high cost of repainting (to get rid of TTC colours) if TTC's contract is terminated or expires.