It is amazing that we used to send thousands of pounds of tobacco across the world on year long voyages with nothing preventing them from getting air, except maybe a barrel or a canvas tarp over a palette. Isn't this where many have said that the concept of aging came from? Then, we only had small amounts sold in little burlap drawstring bags for a few hundred years. Now, we have it down to a science, with no real studies done to support, but well thought out hypothesis nonetheless.
The reason I remove the rings, is to assure myself that the seal has set. Plus, this is how I was always taught to can. I run the jams, jellies, tomatoes, green beans, etc... Then before I put them into the pantry, I remove all of the rings. If a sauce spoils, I can easily tell by how it pushes up the lid, and I don't have to wait for the sauce to ooze all over the shelf before I notice it.
Rings provides a false sense of security. They are designed so that while in the canner/pressure cooker, air can escape the lids, but still hold the lids in place. They do not provide much pressure to hold the lid in place tightly, some other pressure is needed to set the seal. In tobacco canning, the pressure comes from the microbes using up oxygen. If a lid loses a seal without a ring on it, it would just as easily lose the seal with the ring on. So, it merely provides a false sense of security that is not detected until the ring is eventually removed.