In the event that two dogs are saying this, often there is a scrap. But by your dog rolling on the ground and exposing his tummy, he is making sure no mixed signals are sent and that all will go peacefully. Most animals are not born to love being under restraint. In many areas though, the leash serves a useful purpose in making sure our dogs are kept well away from the traffic. However the leash can translate into a very powerful medium of discussion.
Many younger dogs like to pull on the leash and walk out in front.
In this case, it is just the dog's desire to work. It is important to continually remind your dog in a gentle, firm and consistent manner that you are the boss and in both situations training classes can help sore arms and egos. Wolves, the forebears of today's dog, were predators and a large part of many predators' roles is scavenging. As a result, this trait has carried down to our dogs and they will occasionally steal unless they are taught not to. Training your dog to remain in a down or stay position while you leave him with little tidbits can be a very useful tool.