Because Dai-Shocker certainly hadn't been just shown to attack multiple worlds so there's no way Double could have learned about them... It was never shown how neither Eiji nor Shotaro learned about the situation before their cameos, so I don't see how one was any better than the other in that point.
If Eiji can watch Eternal's announcement off screen and somehow get one extra medal from Ankh, Shotaro can see some Dai-Shocker troops attacking and then get the other necessary information about their apparent leader from Philip.
What bothers me the most about Double's scene in All Riders is how tacked on it feels production-wise. It wasn't even recorded in the same place where the other All Riders vs Dai-Shocker scenes were done... They used the tv show rider war area for it, and the difference is really obvious. It's clear they recorded the Double scene after everything else and didn't want to go back to the movie recording area, just using the same area that would be used by the tv show some time later. I wonder if they ever got around to recording some part of that scene without Double before doing it with Double? Too bad Toei never reveals scrapped scenes like that...