having worked in the automotive maintenance industry for a period in my past, it does happen. It usually happens when the tire sits flat for a long time and the bead comes off the rim allowing rain water to accumulate. A careless owner may try to just pump the tire up (it will take some effort to get it reseated). It will be very difficult to remove the water while the tire is still on the rim. The water in the tire will make it impossible to balance...

Also note that most of that "fix a flat" goo that you squirt into your tires will also have the same effect. It makes the tire practically impossible to balance because it stays gooey and will slowly move around the tire...especially when it sits for a period. You may have some of that goo in the tire too. I think the newer stuff is better about this though.

Goodyear once made a tire that had a layer of goey tar like substance on the inside of it and they heralded it as the no-flat tire. While it proved to be very resitant to puncture, it proved equally resistant to balancing and was quickly removed from the market.