Also, Superman and Clark Kent have been seen in the same place at the same time many times. Clark can easily get another hero to pose as him. Pre-crisis it was Batman. Post-crisis Matrix posed as Clark several times and because of her Superman and Clark were photographed together a number of times. It was a big news story that Superman had rescued Clark after Reign of the Superman, complete with a Jimmy Olsen photo of Lois with Clark and Superman on either side of her.
In the Red Robin series they had Vicki Vale figure out that trick so Tim also faked a crippling injury that Red Robin clearly didn't have.