Originally Posted by Andy M.
In this case, the brand of all purpose flour is less important than the fact that you are using all purpose flour rather than bread flour which is higher in protein or even bread machine flour which is even higher in protein.
Jeff Hertzberg, who authored "Artisan Bread in Five Minutes a Day", mostly agrees with you, and says you can generally use what you like (for bread, anyway). The exception: "Be aware that King Arthur All-Purpose Flour has a protein content of 12 to 13 percent, solidly in the range of high-protein bread flour rather than all-purpose."
For pizza dough, you can find recipes calling for either. I use bread flour for pizza, mostly because I regularly make no-knead bread and always have a good supply of bread flour on hand.