Wrong. There is at least one exception. Kansas City Royals baseball fans can bring their own food and beverages into Kauffman Stadium. According to what I was told, the only restrictions are that the food items must be carried in bags or soft thermal containers -- nothing made of glass and no hard-surfaced ice chests.
That's pretty cool. And it's likely to encourage more fans (especially those with children) to attend games because bringing their own sandwiches or other snacks keeps the costs manageable.
BTW, I ate one of those $4.75 hot dogs at Kauffman Stadium, and it was pretty blah.