People can breed whatever they want and call it anything they feel like. They can buy and feed whichever version of any given breed they care to. If they bought an AB, they have an AB. There are papers proving their claims in most cases.
IF the breed is a boardog, then every single AB should be of such heritage. If it protects, cool. If it works man like a heathen, but won't catch... Is it an AB? Will it fight, but won't defend? If it's a bulldog and an American Bulldog on top of that, the dog [u]must be one[/u]. If you want to add papers to such a dog to "elevate" it from the common pigger class, knock yourself out. All the better. However, hundreds of litters born to parents not belonging to the same breed (not so important), same type (somewhat important) and the same working background (very important) can all have the same papers.