I'm leaning towards a bent wheel.
It'll balance out on the tire machine, but put weight on it and it can come and go with differentiating speeds.
Dually wheels are especially susceptible to this problem, due to their extremely off-centered design and the fact that many have been overloaded or abused.

The wheel can be center bent, or rim bent.
A person runnning the tire/wheel balancer SHOULD be able to catch this, but some of these folks are pretty dim.

Mark.