The line is not taken out of context. That is Flowers's solution to the problem. The idea that the alternative is God playing both sides of the board is his idea too. It is not the answer Calvinism gives to the problem of evil.
@atpollard posted Gill's explanation and I think it is a good one.
I'm not much of a Calvinist but the problem of why is there evil is a question we all face if we talk to anyone who is a skeptic and I just think that in this case the Calvinist explanation is the best one I know of. Flowers and Turek are arguing against an extreme determinist view that is not the way Gill or Edwards would explain it. According to their argument a Calvinist says that God must directly cause evil or an evil bent of mind in humans or even in Lucifer.
Read Gill's explanation. It is difficult in some of the concepts but it does make sense. Maybe he's wrong but I would like to see someone post something that refutes that view at the level it is presented, not by simplifying it and then refuting the resulting position. Frankly, I don't mind if in the end one throws up their hands and appeals to mystery. But if you won't accept that and you reject the view of Gill you are left with 2 choices. Either God directly causes all things, even evil, or God does not know what his free will creatures are going to do next because the "decision" does not exist yet because, as you say, they could always decide differently.
Actually I do not think Flowers and Turek were arguing against extreme calvinist determinism. That is the view that many calvinists have put forward. God to be sovereign has to determine all things or He is not sovereign. How they put it is God is "absolutely totally sovereign". AKA divine determinism.
You say you like Gill's explanation but I prefer the biblical one. God is sovereign and man has a God given free will. God is omniscient so He knows all the free will choices that man will make. If man does not have an actual free will but rather that determined free will of calvinism then how logically can man be responsible for those determined choices. It is not a mystery except in the minds of those that can not accept man's God given free will.
Dave you are trying to setup a false dilemma. You want an either or choice but the options you present are not what we see in scripture. Under calvinism God has to determine all things. "God hath decreed in himself, from all eternity, by the most wise and holy counsel of His own will, freely and unchangeably, all things, whatsoever comes to pass;" LBCF 1689 CHAPTER 3; OF GOD’S DECREE
Of course they then have to add the contradictory statement that they really did not mean all things just some things. "yet so as thereby is God neither the author of sin nor hath fellowship with any therein;2 nor is violence offered to the will of the creature, nor yet is the liberty or contingency of second causes taken away, but rather established;3 in which appears His wisdom in disposing all things, and power and faithfulness in accomplishing His decree."
So what we see in the LBCF is God causes all evil but He does not cause all evil and why is that? Because of second causes which so happen to be decreed by the calvinist God. So even when they try to avoid the decree of God it is still the decree of God that determines all things.
But the bible is thankfully not dependent upon calvinism. God is omniscient so He knows all things that man will freely choose to do. He does not cause them to do them and is not waiting until the free agent exercises his free will to know what the agent has done.
So yes the agent could have chosen A or B but whatever the choice would turn out to be that is what God in His omniscience would have know the agent would in fact choose.
If determinism is true and God wants all to come to a saving knowledge of the truth then if we do not have free will with which to reject that offer way are not all people saved? Now I know that you reject the idea of determinism but that is a main tenet of calvinism so needs to be dealt with..