Once again, the dogs see things from a different perspective than people do. Time is a human construct: without the human mind and the human invention of the time piece, there is no time. Dog's don't understand that when they chew the couch at 10 a.m., when they are alone, that at 6:00 their owners will get upset when they return home to find the couch in a shambles. Without that ability to tell the passage of time, actions and their consequences aren't necessarily paired UNLESS they happen within seconds of each other. If you're speaking strictly from the point of view of behaviorism, that is why the timing of reward and punishment is so important. If you want your dog to sit on command and he begins the action, you want to be sure that his bottom is on the way down and impacting with the floor when you say "yes!" or click your clicker instead of his bottom being on the way up again. To a dog to know what "sit" means, it needs to have the immediate proximity of stimulus, action, and consequence before it can understand the sequence.
As an example, when I was training my first dog for obedience--a Dalmatian--to heel, it was in the old days of using the slip collar as a correction, in conjunction with a verbal command. If she sat automatically when I stopped walking, I praised her. When she did not sit automatically, I snapped the lead and said, "NO, Gypsy, SIT." At the same time I pushed her bottom down. This process went on for at least a week before she "clicked" on it and we moved on. Fast forward a few days. We are in the kitchen and she is cutting up as I try to feed her. I said, "NO, Gypsy!" and she sat. To her, the proximity of those words led to the action "sit," which would then garner her quiet praise. That is, "sit" didn't mean sit and "no" didn't mean "no;" they were one in the same and led to her performing what she thought was the correct behavior.
So, when you leave the house and Rover sees you go, he doesn't think, "I now have ten hours in which I can perform mischief, so I'm going to take a nap before I eat the couch, after which I'll nap again in a soft pile of stuffing." No, he goes about his doggybusiness until something motivates him to chew the life out of your couch--maybe something that smells good got spilled on it or a microscopic imperfection invites him to enlarge it--who knows? Then once he feels satisfied that the couch has been improved sufficiently, he'll go to sleep and forget all about what motivated him, what he did, and so on. When you finally walk in the door, he runs to greet you because that stuffing that is strewn around the living room means nothing to him. It is not until you respond in anger that he understands that something is wrong, although he doesn't understand. He responds submissively: one front paw is probably raised, his ears and flews are drawn back in the stress position, he lists to one side as he prepares to fall and expose his belly. Stay angry and when he falls over he will urinate for you. To us, that looks like guilt; to him, it is self-preservation.
So what does it mean when your dog comes into the room and automatically starts exhibiting those behaviors? Isn't that guilt? No, that just means that he's heard you say, "what the [fillintheblank]?" and can smell that you are angry, even from the other room. He doesn't know why you are angry and in no case does he associate it with the couch, but he knows that he must make you happy because you are the pack leader.
So no, dog's don't feel guilt. Do they feel sympathy? I don't know. I know that they can be away when a member of their pack is not feeling well and they will snuggle, but I don't know if that's sympathy or another means of helping with pack survival. In either case, it works out well for the pack member, so I don't know if the distinction is relevant. I understand the need to put things in human terms, so that we feel that we understand them, but sometimes anthropomorphizing our dogs does them more harm than good.