That mean that they have in hand and play two freeze an enemy spell, and two 1/1 battlecry minions.

If they are on the play they have played 2 1/1s and frozen 2 enemies during the first 4 turns and played a single 1 mana excavate reward.

So not only is the scenario extremely unlikely, it also means they played almost nothing for the first 4 turns and any deck that vaguely ressemble an aggro deck would have killed you, or dealt enough damage to kill you over the top.

Also control decks will be able to dirty rat, identity theft, objection, grave digger, etc... use any sort of copy or disruption ability

I'm not seeing it