I don't really believe in the revenge pee either. A dog may pee because it's stressed or upset, and who is to say whether the dog is just upset, or upset with YOU in particular. Getting a new sibling is stressful (and releases hormones), and as humans we understand that the new dog is not going away, so it's easy to assume the dog is expressing its resentment. I think dogs are pretty direct, though: if it doesn't like the new dog, it's more likely to simply attack the newcomer, beg for your attention, or bark.
As
Nancy1999 said, dogs often lose training when they move to a new house. Again, as humans, we think of moving as exciting and stressful, but not something to cause resentment. But the behavior is the same. Why not say the dog is peeing as a way to complain about his new surroundings?
Also, it's important to make sure you aren't inadvertantly reinforcing bad potty behavior. If your dog pees when you're gone, he may notice that pee tends to keep you around - he gets some attention, albeit negative, you may take him outside to go, and you'll hang around to clean up the mess.
People tend to personalize barking as well. When our dog barks at us, we assume that he knows how annoying he is and is using it against us. Of course, dogs don't see barking that way at all - they are using a basic way to get our attention, and for some reason, we haven't noticed yet. If we train them well, they stop barking because they realize it doesn't work, not because they see that we need to get up at six am for an important work presentation.
Now all that being said, Thor's previous owner had a boyfriend who was not particularly fond of him. She told me that once when her bf picked Thor up from a particularly stressful grooming session, Thor lifted his leg and marked him! So I'm not going to say for sure that dogs don't understand revenge.
