Christ never told Satan that they weren't Satan's to give to anybody. I've always taken that to mean that the kingdoms of this world do belong to Satan,
Creation belongs to God, I think we can agree here.
God gave who "dominion" of the earth? Man, not Satan.
But, Who is the Prince of this world? Satan
If Satan is the Prince of this World, from whom does he get dominion over all the kingdoms, to tempt Christ? One might conclude he gets that "power" not from God, but from Man. Through our 'freewill' we give our power to Satan and set him over us as the Prince of this World.
How sad that last temptation must have been for Christ, as he looks out at all the kingdoms that have surrendered to Satan.
Now go back to what I said about politicians tempting the citizens, and they bow down and worship the government. We give him power over us in exchange for earthly happiness, we surrender our Godly duty to have dominion over the earth. So yes, it is evident to me Satan does have the authority to offer the riches of the kingdom.
Jesus tells him what? "Again, the devil took him to a very high mountain and showed him all the kingdoms of the world and their splendor. "All this I will give you," he said, "if you will bow down and worship me." Jesus said to him, "Away from me, Satan! For it is written: 'Worship the Lord your God, and serve him only.'
This last temptation is a huge warning for us. A wisdom to be careful regarding the riches of kingdoms in this world..and to not set them over us, for to do so places Satan in the position of worship. And Jesus says what to Satan? "Away from me, Satan! For it is written: 'Worship the Lord your God, and serve him only.'
Pretty powerful insights into these 40 days of Lent.
I think that’s largely correct.