It seems to me as if the check that an assignment makes for each required Duty Officer slot is independent of the other slots.
Meaning, let's say I have a shipboard diagnostics assignment that requires 3 Operations Duty Officers. If I have 1 available Operations Duty Officer, the system will let me accept the mission, because that 1 available Duty Officer could potentially fill each one of those individual slots, not taking the other 2 slots in consideration. However, obviously that 1 Operations Duty Officer could not fill all 3 slots simultaneously. Therefore I cannot actually complete the mission.
I hope this makes sense.
Also, I hope I'm not double-reporting something, but I could not find another mention of this.
There was one today that needed 5 colonists. I have 3 total. It still showed without the red mark. I put in the 3 and can't do it as I'm 2 short. The Tribble free C-Points to play in the c-store I blew it all on more officers. I got other civilians but no colonists so couldn't do that sweet 6 hour one.