Brachycephalic (Snub-Nosed) dogs and cats are very sensitive to high temperatures and will not be accepted when temperatures at any point on the planned itinerary exceed 75 degrees Fahrenheit (24°C).
The following breeds are included in this restriction:
American Straffordshire Terrier
English Toy Spaniel
Japanese Spaniel (Japanese Chin)
Straffordshire Bull Terrier
I don't really think of the Pit Bull as having breathing problems anywhere near that of a Pug, EB or Peke.
And they should definately add the American Bulldog (Johnson type) to their list!!!