Relaxin',
Its their policy and property, and clearly stated on their website. And security checks out the car on the way in. In Ohio, you can't bring your own booze into a bar or food into a restaurant if the premises have a food license and/or liquor license.
Other states have different rules. In Florida, at least when I was stationed there, up until 2AM you had to buy booze by the shot, but after that you could bring your own bottle if the bar had a "bottle club" license. They kept your bottle behind the bar with your name on it and sold setups. There were several occasions when I walked out of the bar into blinding morning sunlight.