It's somehow in between public and private; it certainly receives substantial funding and support from the state of Michigan and the federal government. I don't think it's obvious that they should be prevented from gaining financial advantage from research activities (but there are certainly people on both sides of that question).
A prerequisite to a free market is perfect information. Insider information makes markets imperfect, thus losing the sort of holy grail property of getting the "right" price for a good.
Any gov't entity ought to, when possible, Yes.
For certain, the terms by which these reports are made available ought to be disclosed to all parties. No party should be arbitrarily or "accidentally given" an advantage over any other.
So there are no free markets? Perfect information is just a theoretical benchmark used by economists, not something you'll ever encounter in real life.
>Insider information makes markets imperfect, thus losing the sort of holy grail property of getting the "right" price for a good.
What a load of nonsense. Just think for one second about what you wrote: not incorporating information into the price makes it "right"?
It's not used as a benchmark. It's used as an assumption when building (largely wrong) neoclassical mathematical models of the economy.
And yes to your larger question, there are no and have never been any free market in human history. I would challenge you to name one, if you can.