That's not necessarily true. I'm sure there are cases involving government subsidy wherein the owner retains full private property rights. Receiving a subsidy certainly doesn't automatically constitute an automatic waiver of such rights.
I suppose State laws vary, but in Virginia, with some exceptions, if the stadium/venue avails itself of public funds, then the state gun laws regarding carrying in public places apply.
Schools are one of he exceptions. But not many professional sports teams play at school stadiums or arenas.