"Just to play devil's advocate, if the county builds a stadium for the local high school team, are citizen's entitled to free admission?"

Obviously you are missing the point, going to the stadium is the result of something being on show there, the "content". Therefore, it would not be free. What should be free (excluding maintenance costs which would need to be payed) is the usage of the stadium and actually it most likely is.

I know that in the UK I think there is a data liberation act or something similar, where you can request for data to be made available in public which was payed for with tax money. I think, however, that you shouldn't even need to ask.

If they don't want to publish the data, then don't pay for it with tax money...