What Lindy is referring to is called a lug-centric adaptor. A lot of people who have a Toyota truck/SUV with aluminum wheels have probably encountered a need for this adaptor.....as Toyota wheels are notorious for not being able to balance properly without it.
A little explanation will be required. There are basically two kinds of wheels. You can have a hub-centric or lug-centric....and the name kinda tells it. A hub-centric wheel is centered off of the hub..............and a lug-centric (sometimes called stud-centric) is centered off of the studs/lug nuts.
You can usually just look at the lug nuts for a particular wheel and know if it is hub-centric or lug centric. Lug nuts that have flat surfaces are for hub-centric wheels. All the lug nut need do is to hold the wheel/tire assembly directly onto the hub. The reason there are hub-centric wheels is that it supposedly takes the stress off of the studs somewhat and requires less clamp force. You see a lot of hub-centric wheels on semi's.......and on the newer Ford pickup/SUV's since 1997. A lot of your older mag wheels, that had the lug nuts that you had to put a washer onto the shank of the lug nut, were also kinda examples of hub-centric wheels. Here are some pics for examples:
Now to lug-centric wheels. The vast majority of wheels are lug-centric...or are centered onto the vehicle/trailer spindle by the lug nuts. Most of us are used to seeing the conical or acorn type lug nut for these wheels.
The taper on the lug nut, fits into the matching inset of the wheel.....thus the wheel is centered and clamped onto the hub assembly using the lug nuts.
Now about balancing. Since most wheels are of the lug-centric (centered on the studs), then common sense would say they need to be balanced, using the same method (centered on studs)........right?
Since time is money (especially in the manufacturing process of vehicles), having to mount each wheel onto some kind of special lug centric adaptor just to balance it, doesn't make good economical sense. It is extremely time consuming. That's why even lug-centric wheels usually are made with precision center holes, so they can be balanced by centering off the center hole. You could say the wheel is actually both.... a lug-centric for mounting on the vehicle and a hub-centric for mounting on the balancer.
Now there are a few exceptions, as noted at the beginning with Toyota. They make some hub-centric wheels that just don't fit a hub-centric balancer correctly because of the way the center caps attach to the wheels..........and you need a lug-centric adaptor. This adaptor mounts to the lug bolt holes on the wheel, then slides onto the hub-centric shaft of the balancer. This is what Lindy is referring to.
These adaptors aren't cheap.....as they have to be very precision made since they are for balancing. The last one I had cost about a thousand dollars. You used to have to buy them for the specific bolt hole pattern you wanted, but they are making some universal ones now that will fit more of a variety of patterns.....but you still need a couple to fit the most common patterns. You also have to factor in the fact that your employees may lose them or some of the parts........and you can understand why many tire stores don't have them. It is also extremely time consuming to have to mount the adaptor to each wheel, to place on the balancer, then unbolt it all and go to the next wheel.
Now, IF and I really mean 'IF' the center hole of a lug-centric wheel is not made correct in the manufacturing process, then to properly balance it, you will need to use some kind of lug-centric balancer adaptor, since you can't accurately use it as a hub-centric wheel on a hub-centric balancer. You are not going to encounter this a whole lot, but you could.
It wouldn't hurt a thing to balance all wheels using a lug-centric adaptor......but it's not always necessary. If the wheel is made with a precision center hole, then it can be balanced hub-centrically. This saves the customer in time and cost.
As far as a wheel running lopsided, if the center hole is off center, then that wouldn't be affected with lug-centric wheels. Since you are actually centering the wheel off of the lug nuts/studs...then anything within the diameter of the bolt pattern would be a non-factor. The only way the wheel would be lopsided is if the lug/bolts are non-centered.
However it would jump all over the place if you tried to place it on a hub-centered balancer using an off-center center hole wheel.
I hope I have not clouded the issue with my long-winded post.