I was able to find this PDF which claims that historical evidence gives tangential evidence to the story in Daniel.
He mentions that the names of these three people are found on a 5 sided clay prism from Babylonia, but so far I've only found Christian sites that make reference to this pillar. It seems this story plays a much larger roll in Christian theology than it does in Jewish teachings.
A small comment about "public" stories in Tanach. Not all events that were done before all the people, were infact done before all the people of Israel. For example, there is one story of a man forced to be intimate with a women before all the people on a rooftop. Pure logistics would prove this to be impossible. One might say that such a public act would be written about in many places, but on the other hand, such an act might have just been done in front of select people represetting "all the people of Israel" and not have been widely written about.