Remember how the nugget bridge was actually ran by Team Rocket back in pokemon red? trying to get recruits? Red said no, but Blue didn't. Remember the first time you see Blue since the start of the game he's coming down from Nugget bridge, and had already met Bill by that point. So he'd met with the Rocket member. Now does it make much sense for that Rocket grunt to challenge Red when he refused to join, and act like no one has refused before?
Then there's more. The next time you meet Blue after the ship, he's where Rockets are, at the Pokemon tower. Then, he's at the top of Silph tower, somehow sneaking past the guards. Also usually you'd need a card key to get to that point, which only the Silph employees and Rockets had. After that, he inherits the leader, Team Rocket's gym.
so why would he not put on the costume and tell everyone he joined team rocket? if he did, his reputation would be ruined and he'd never be able to win all the badges, become pokemon league champion then a gym leader himself. he'd be too busy being wanted by the police.
blue has a deeper character then most would think.