You lied. Scalia is factually correct, the lease agreement makes that painfully clear.
Scalia is trying to have his cake and eat it to. As the majority argued it, the US has exclusive control over Cuba and are therefore de facto sovereign. If Scalia wants to argue the we have merely leased it and that Cuba is de facto sovereign, then Cuba has jurisdication and can take possession of the detainees. Of course we would not turn the detainees over to Cuba, would refuse to recognize their sovereignty, and therefore we are sovereign.
Sorry, but Scalia is trying to argue an excluded middle here and he falls into the same kind of logical hole that makes some observers believe that Scalia is losing the mental powers for which he is so esteemed.
To me his dissent reads as an emotional rant, not a legal argument.