Daniel Was Wrong

Premil dips (premillenial dipsensationalists) and other fundamentalist prophecy freaks love to discuss the alleged prophecies of Daniel including those in the story of Daniel interpreting Nebuchadnezzar's dream about the statue. According to the story, Daniel, with God's help, correctly told Nebby that he (Nebby) had dreamed of a statue with a head of gold, breast and arms of silver, belly and thighs of brass, legs of iron, and feet of iron and clay. And Daniel explained to Nebby that each part of the statue represented a different kingdom.
Here is Daniel 2:37=38 (KJV) where he explains to Nebby the head of gold:

"Thou, O king, art a king of kings: for the God of heaven hath given thee a kingdom, power, and strength and glory.
"And wheresoever the children of men dwell, the beasts of the field and the fowls of heaven hath he given into thine hand, and hath made thee a ruler over them all. Thou art this head of gold."

This seems to be Daniel's longwinded (and perhaps poetic) way of saying that Nebby ruled over everyone on earth, thanks to God. And this interpretation is corroborated by an examination of Chapter 4 of Daniel, in which he interprets another of Nebby's dreams. In that case, Nebby dreamed of:

"...a tree in the midst of the earth, and the height thereof was great.
"The tree grew, and was strong, and the height thereof reached unto heaven, and the sight thereof to the end of all the earth:
"The leaves thereof were fair, and the fruit thereof much, and in it was meat for all: the beasts of the field had shadow under it, and the fowls of heaven dwelt in the boughs thereof, and all flesh was fed of it." (Daniel 4:10-12 KJV)

And here is Daniel (4:22) interpreting this for Nebby: "It is thou, O king, that art grown and become strong: for thy greatness is grown, and reacheth unto heaven, and thy dominion to the end of the earth."
Daniel was clearly telling Nebby that he (Nebby) ruled the whole world, which, of course, was not true. Nebby never ruled the whole world, and he never even came close to doing so. Daniel, the prophet of the all=knowing God, was just plain wrong.
How come, premil dips? Why did Daniel falsely claim that Nebuchadnezzar ruled the whole world, and how do you reconcile the fact the Daniel was wrong about that with your delusion that the Bible is the literal and inerrant word of God?