I would guess what with there being two "doctors" around, one might be technologically geared, and one might be the medical type. You'd want both on a spaceship! Or on any long journey, in fact. I always thought of Chief Vermilion as being the "head of security" type person... except, since he's the only one around, he's just plain security. I think he's a bit to loopy to be the leader of any kind of team, but he probably does a fine job on his own! He's certainly got the fearlessness needed to deal with space pirates or... giant space elephants or whatever hazards they normally encounter on their travels. Speaking of which, what do they normally do on their travels, when they're not getting sucked into alternate dimensions? Are they the Starfleet of their world? Or is the D.S.S Souleye a privately owned vessel, for running errands?
This is one of the things that makes VVVVVV so freaking great. Go look at a screenshot of the game that we're talking about. Then look back here and see what type of discussions we're having about it. Who would expect that, going in?
EDIT: Well, my memory is terrible. Turns out Vermilion's title is "officer", not "chief." Verdigris is the chief, so I don't really know what that means. "Officer" seals Vermilion's role as the leader/peacekeeper type, though.