Because it's not on cooldown for everyone. It's a triggered cooldown for people who have recently participated in the same PVE/STF. It's just there to keep you from running the same one over and over.
For example: you play Federation Fleet Alert. After completing it, open your queue, and you'll see a cooldown on Federation Fleet Alert. Doesn't stop other people from queueing for or playing it - just you (and the people you were in it with).
FYI, it doesn't even carry over to other characters on the same account.
Member of Special Operations Command
and Foundry author (first mission published July 2014)