In my opinion, lapping rings is as important as bedding the action. (For purposes of discussion, I consider Burris signature to be "lapped.")
Rings do not have to be lapped. Actions do not have to be bedded either, but they both make a huge difference in accuracy. A guy I shoot with has worked for several scope companies, (he is in high demand). He says almost every scope that comes in for warranty work has a bent or dented tube from being mounted in un-lapped rings. He said once they are bent, dented, or deformed, they will never be the same.