Real random picking doesnt exist. All random number generators are approximations. Some generators are better then others. That might be the root cause of non uniform outcomes.
Random is independent of your previous picks. It isnt influenced with civ pickers afaik. Random is only affected by other random pickers.
So if player 1 picks Huns and player 2 picks random, then p2 can still end up with Huns.
But if player 1 picks random and gets Huns and player 2 picks random again, then p2 cant get Huns.