Yankee Stadium and Shea Stadium in New York City are clearly "public venues," since the City of New York is the legal owner of both facilities. A different situation could occur (and does occur more frequently these days, as these venues get more expensive to build) in other places. If a corporate entity such as the Ballpark at Arlington is listed on the property title as the owner then the stadium is no more a "public venue" than the Wal-Mart across the street.
I said it was well-established and uncontroversial as a point of law. It has been thus since the founding. You may feel free to disagree, but President Bush is on perfectly firm ground to speak out on this ruling notwithstanding the perfectly well-established and uncontroversial exercise of eminent domain that he's been associated with.