The common advice that a dog should walk beside or behind its owner is likely based on owner training and learned consequences, not inherent dominance.

“I think that there's a lot of learning occurring of course that you teach the dog that if you stay at my side or behind me then you know there won't be any unpleasantness but if you pull ahead head, I'm going to yank you back. So, there'll be an unpleasant um uh consequence to the pulling behavior, which will then influence the animal's choice in staying next to you.”