You'll have slop in the driveline that will allow things to turn. Try pushing sideways on the driveshaft near the carrier bearing, it should move some but if it moved freely that could be your problem.
I just changed my u-joints and carrier bearing, be ready for sticker shock when you buy the carrier bearing as it is a dealer only item. I had 151,000 miles on the truck and everything was original. My rear most u-joint was pretty dry and sticky and the carrier bearing was shot. I was getting a vibration some of the times at a certain speed, somewhere between 45 and 55 mph. It didn't happen all the time but I would have to speed up above 70 to get it to go away.
If this is a job you are going to do yourself have torches ready in order to get the carrier bearing mount un-done or at least spray down the bolts a few days ahead of time.