Four hundred and thirty crew sounds like a lot of people, enough for four to hide among, yet wouldn't someone
notice that there are four new faces (or at least two, since O'Brien and Bashir worked together, and Sisko and Dax were the other team), wandering around all of a sudden
I mean, I've never known everyone
at my workplaces, yet I knew everyone's face and generally knew when new people were brought in, so I wouldn't get suspicious that there was someone hanging around who shouldn't be. But here are four people who shouldn't be there, and just because they're dressed in the right uniform, no one questions it.
I suppose the same thing happened with Norman the Android in "I, Mudd". How many days was he there, wandering around in a uniform but generally being odd and suspicious? Was it three days? And only McCoy complained!
I get the feeling that anyone who wants to serve on a starship or hijack it need only put the right tunic on.