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.
'91 Toyota Pickup
'09 Kawasaki KLR650
'12 Gunnar Rockhound 29
"To live is to suffer, to survive is to find some meaning in the suffering." -- Friedrich Nietzsche