Yes, it would seem that the dog's owner would be liable, but if there were multiple passengers with dogs, how would they know which dog did it?
I'm an avid dog lover myself, and I think that any dog owner clearly knows that dogs make messes. That's something that happens with almost absolute certainty, unlike a bottle of wine or perfume which probably won't break 9 times out of 10.
With dogs, however, we know that there's going to be a mess if they're kept in close quarters for several hours. That's something that anyone should be able to anticipate and prepare for. (We can expect that with dogs, but not with humans, which is another story altogether.)
Personally, if I absolutely had to take my pet with me, I would most likely drive instead of fly. That way, I can just have the pet with me in the car and not have to worry about what might happen in the cargo bay on an airplane. I just don't have the heart to subject my dog or cat to that. There are rest areas every couple of hours, and many hotels will accept pets. I'd rather do that and keep my pet with me than having him sit in terror in some box in a cargo bay where he has no idea what's going on.
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