Emailed my local Extension office about the ring/band discussion, here's their answer

Based on this comment thread, I emailed my local extension office to see what they had to say. Here's the answer I got back:

Jars are most properly stored without the rings, this prevents rusting of the rings (bands) due to trapped moisture and facilitates seeing when/if lids lift on jars and the jars become unsealed. Loosening the rings is also OK, but I always find that I need the rings for canning the next day, etc so I simply remove the bands altogether. It is important to wipe the threads and inspect the seal (after the jars have cooled) prior to storage.

The time when the bands should be on jars is when they are transported, i.e. to a farm market, as a gift. This prevents jarring of the seal if jars knock against each other in transport or handling.