Yep and not only that. Is not necessary that you hit 60 seconds to be matched with a random player. It's enough that one between you and the player you are matched with hits 60 seconds for it to happen.

So is very possible that is your enemy that hit 60 seconds and that you get matched with him just because you were the guy in queue at that specific moment even if you didn't reach 60 seconds of queuing time.