I would replace the bearing(s). Too much play in the bearings allowing the axles to wobble is one of the reasons why the rear axle seal fails. Your Tundra doesn't have a million miles and hasn't been abused, so stuff like flexing of the housing doesn't make a lot of sense. OTOH my axle was still running the bearings that Toyota put in up until a couple of years ago, so anything's possible.
"Why does the U.S. care which flag will be hoisted on a small piece of land thousands of miles away?" -- Ron Paul