The order of operations does indeed state that exponent precedes subtraction. The negative sign there isn't an operation though (or at least that's how I understand it); it's part of the number, a symbol to denote that this number is negative.
What's more convincing than my speculations though is Microsoft's PowerToy Calc and Google. If you enter the expression "-2^2" in either of them, you get 4.
I searched Google for info on this but I found mixed answers, unfortunately not from reliable scientific sources.
