"would be to think that satan actually had that ownership, and the authority to give it to anyone."
The "World" does belong to the devil - the pride and glory of worldly civilizations. It was forfeited by man at the fall. And of course he has it by God's permission.
"Do not love the world or the things in the world. If anyone loves the world, the love of the Father is not in him. For all that is in the world-- the desires of the flesh and the desires of the eyes and pride in possessions--is not from the Father but is from the world." - 1st John
Satan is still the "god" of this world...
"And even if our gospel is veiled, it is veiled only to those who are perishing. In their case the god of this world has blinded the minds of the unbelievers, to keep them from seeing the light of the gospel of the glory of Christ, who is the image of God." 2 Cor 4
NMP.