I believe that my dog felt guilt, because when I would come home and find he'd gotten into the garbage and strewn it around the kitchen, he would use body language very similar to that of a human who was feeling guilt. (The dog was not picking up on my emotions, because I usually hadn't seen the mess yet, and didn't know what he'd done until his body language told me.)

This body language has much in common with submissive body language, which is partly shared between canines and primates.

So ancestral "guilt" could have been "the emotion you feel after disobeying the alpha", which helps you display submission and also not do it again so you don't get beaten again. It could originally have just been a type of fear. (Perhaps it still is!)

This is compatible with Yvain's explanation - it would have the effect Yvain described; consistent guilty behavior would provide evidence that you would be likely to obey the alpha even in his/her absence. But the origin could be simpler than that.