T certainly appears that Nebuchadnezzar did exactly the wrong thing with the knowledge that he had gained in his prophetic vision. You should recall that in Daniel 2 we read about how God assigned to Nebuchadnezzar the "privilege" of being the head of gold on the image that represented all of the kingdoms of this world. Such news should humble a man (as he realizes that he is unworthy of such attention and influence). Nebuchadnezzar decided instead to construct an entire image of gold (90 feet tall), and to establish a new pagan religion around it. Most likely, it was an image of himself. How typical of the demagogues who have always ruled the kingdoms of this world.
Nebuchadnezzar had the pride and gall to demand that all of the most important people in his empire come to worship this statue. The motivation for obeying the pompous king was a very real threat of being barbequed alive (vs. 6). Now, we do not know where Daniel was or why he is not mentioned in this story, but his three friends attended the worship service in obedience to the king. But in defiance of the king, they refused to bow to his idol. Not surprisingly, someone tattled on them. But they didn't care. Even though the king "mercifully" gave them a second chance, they still refused to bow. In fact, they boldly claimed that God could save them from the flames, but that even if He wouldn’t, they still intended to maintain their loyalty to Him (vs. 16-18)! Well, they were condemned by the king, but the King of kings saved them.