You see, I would've bought that explanation ten years ago (anybody remember the Bat-Embargo?). However, did the CW network not just produce a widely popular crossover in which the characters met different versions of each other, some played by the same actors as completely different characters???
If audiences could understand that the three Superman are all from different dimensions, despite one Superman looking identical to the Atom, I don't think they'd have any issue with Green Arrow and Speedy. In a world where Cinematic Universe has become a part of the general public's vernacular, I don't think I'll be accepting that argument any time soon.