One thing to remember with these breed bans is that they require the identification of ALL dogs down to a specific breed. When you have a mix-breed dog, this is pretty much impossible to do in an accurate manner. It comes down to "what breed does the dog look like".
Some insurance companies won't allow you to identify a dog as a "shepherd cross" or "lab cross". They insist that you pick a second breed and call it a "shepherd boxer" or "lab dingo". The problem is that most mixed breeds have more than 4 breeds in their background. So, again, it's all down to appearance.
There are also poorly bred purebreeds. I had a purebred boxer as a kid. She was all white, her muzzle was too short, her ears were down, her legs were too short, etc. She was always falsely identified as a "pitbull" (even a boxer breeder had to ask if she was actually a boxer).
You can't trust statistics that are based on faulty observations.
As for the OP, it does sound like she failed to clarify her situation. Either way, as I have 2 large mixed breeds, I always put a ton of clarification into these situations. Once I got the verbal OK on the phone, I would have sent the check in with the deposit with a note that restated the phone agreement and a statement that by cashing the check the park agrees to allow my (insert breed/breed-mix) dog during our stay at the park with no additional requirements.