Take it from someone who has mounted and balanced more tires than I can remember: you can *balance* something perfectly, but if it is not round, it will shake no matter what.
This is why when I spin the wheel/tire combo on the balancer, in addition to watching the numbers, I LOOK at the assembly as it spins. If it wobbles, that is an issue. Cheap tires, tires that sat for a long time, old tires, anything made by Goodyear, are all going to be suspect and thus need extra scrutiny. But I have had bad tires from just about every manufacturer, even Michelin (although that is pretty rare). Sometimes a slightly bent wheel is the cause too. If there is ever any question about a wheel being true, I spin it up WITHOUT the tire mounted and watch the rim closely for a wobble.
Road force variance balancers are even better, because they do something "regular" balancers do not do. They actually load the tire on to a roller and measure the force as the tire rolls. They can detect things that even the naked eye cannot. Also, most of those machines have two stage balancing ability, where they can spin the tire at a higher speed to verify balance.
Related story: my brand new Sprinter's OEM Kumho tires were so bad the van was virtually undriveable. It had a jerk in the steering wheel starting around 10 MPH, and by 40 it was shaking the whole van. I could have sworn it had a bent wheel. Nope, 3 of the 4 crappy Korean tires were shaped like ostrich eggs.
New set of Continental Vanco tires and it is fine.