I highly doubt the Humane Society paperwork can prove anything.
Most of the paperwork is educated guesses since most dogs are brought in or rescued from abusive homes. At best I would say that paperwork could convince people that don't know anything about dogs but I would not put any stock into it. Most of the time it is up to the landlord/airline/person that bans breeds anyway.
Most dog adoption places that I have come across usually put "mix" or "unknown mix" or another type of dog for pit terriers because of the bad press surrounding them.
I would also like to point out that the reason they ban them on international flights is because they are outright banned in a lot of countries. I am not positive, but I doubt you can fight the law in those countries with Humane society paperwork, especially when they told you that it was a terrier mix.