The problem is not the balance machine, or the tech using it , or the wheel (usually... they do get bent...) , or , in most cases, even the tire.
The problem is that properly BALANCED wheel/tire assemblies can, and often do, vibrate at higher speeds... balance is only one part of the smooth equation.
i once severely flat spotted a tire locking up a wheel at high speed on dry pavement... I was young and dumb... and took the car in to a tire shop because of a vibration. The owner was kind enought to tell me how you can "balance" any wheel assembly, but that doesn't mean it will run smooth... my wheel showed nice zeros on the machine, but vibrated badly at high speeds, because the tire was not ROUND anymore. And ALL wheels and tires have some degree of out of roundness... even brand new ones.
When a car maker purchases wheels and tires, they do everything possible to get that NEW CAR ride and smoothness. These include... all wheels are measured and tested for run out , and are then MARKED at the low point. Wheels that don't meet the required spec are not used in production. Unfortunately, this mark is often a sticker, and after the car is delivered, the mark is lost forever. This is an issue when you replace the factory tires later...
Tires are similar. The car maker has specific quality specs for roundness and road force measurements, and again, tires are tested, and MARKED, a red dot shows the "stiff" spot on a tire, or the high spot. Tires that don't meet the spec are again not used for production.
So, your original wheels are measured and marked, along with your original tires, and they all meet very strict tolerances defined by the manufacturer. When they are mounted, the low spot on the wheel is matched to the high or "stiff" spot on the tire, and the assembly is tested again for smoothness on a REALLY EXPENSIVE ( 500k + ) machine. Any assembly that is outside of specs is not used.
Go to a new car lot, and look at the wheels and tires. You will often see bright green stickers on the wheel, matched exactly with the red dot on the tire. Or , sometimes a paint mark, or dimple on the wheel, again matched exactly to the red dot on the tire
Now, you need new tires... and this is where the problems can begin...
Your new tires may not be marked like the oem tires were. So you may not know where the high or stiff spot is. And, these tires may not be as precisely made as the oem tires, so that high spot may be higher, the stiff spot stiffer, so it is even more important to match them up... and your tire store may not have a clue, or not care, anyway...
Then you mount them on the factory wheels, except the sticker showing the low spot is long gone, so they are mounted blindly, not matched to anything.
They will BALANCE, but they may not run smooth. If the low spot of the wheel is not near where the high or stiff spot of the tire is, the assembly might vibrate, yet be perfectly balanced.
If you have a vibration after new tires, do the following:
Check the balance... do not REBALANCE. Most shops will remove the weights first, then re-balance the assembly. No no, Leave the weights on, and re-spin. If the machine shows zero, then you know it is not the "balance", but is an out of round or road force issue. And on new aftermarket tires, it usually is...
If the tire shows as balanced, rotate the tire 180 degrees on the wheel, and rebalance. This often cures a vibration issue, as you have moved the high spot on the tire to a possibly lower spot on the wheel.
Better, if possible, is to try and find a shop with a Hunter road force balancer, and a trained, patient tech to use it. These machines measure the wheel, and the tires road force, and allow the tech to better match the wheel low spot and tire high spot, and hopefully get a smooth ride out of the assembly. These machines cost about 3x or more what a regular balance machine does, and can take 2 or 3x as long to "balance" a wheel/tire assembly... so many shops don't bother.
I have had problematic tires balanced numerous times as well, and blamed the machine, or the tech, or the tire... until I learned that a tire can be properly BALANCED, but not run smooth and free of vibration.