Balance is not the only thing that causes vibration in tyres and rims. Most people think that just because a wheel vibrates that it is "balance" that's causing it. The fact is that lateral and radial "run-out" in a tyre or rim is far worse.
Several things contribute to tyre/rim run-out, one is obviously a slightly bent or buckled rim (the NZ guy that I used to work with one day said that the car he was working on had a "bunt rum"....took be ages to work out he was saying "bent rim"....

), the second is a poorly manufactured tyre where the tread has been laid incorrectly or inner belts/plies have been fitted badly (during manufacture and therefore is a quality control issue) or it's hit something and damaged the belts/plies which is called a "separation" because it causes the tread to separate from the plies (usually), the third is poor fitting where the beads have not been "seated" against the wheel flange and the last is slight radial or lateral run-out in both wheel and tyre but when fitted in the same spot/location cause a big run-out problem.
A good tyre technician will run the rim up separately on a balancer, when they have removed the old tyre, just to visually check for run-out. Once he/she knows the rims is OK he/she would fit the tyre to the rim and align the manufacturers marks. There is usually a white dot which you aligned with the valve however some rim manufacturers have a balance mark(looks like a drill mark in the rim) where they recommend a tyre be aligned with that also has been separately checked (which has a yellow dot), and the yellow dot aligns with this mark.
After the tyre has been fitted the fitter should spin the tyre up and visually check to see how much out either radial or lateral run-out is in the tyre/rim. You can measure the run-out but visual is pretty accurate and much quicker. If there is more run-out in the tyre/rim assembly then you think is acceptable, the best thing to do is "Crack and rotate" the tyre 180 degrees on the rim and run the tyre up again. If this doesn't get rid of the run-out try cracking and rotating the tyre 90 degrees and so on till you get it right. This is called "rotationally matching" the tyre and rim assembly. If the run-out is greater then your little hearts desires then get another tyre and try again. If however you continue on with this process and find that all the tyres from that manufacturer have "run-out" then you know you have been trying to fit a Dunlop tyre to the rim ....

...sorry...just kidding... but it is true that some manufacturers quality control is far better then others and subsequently some manufacturers tyres have no run-out at all....you just gotta find out which manufactures that do.
The thing that differentiates run-out from a balance problem is speed. Run-out gets worse the faster you go because obviously the tyre isn't round so it vibrates and wobbles more and more and more.
Balance on the other hand usually only occurs at constant speeds and can come in and go out at various speeds like come in at 60km/h and go out at 70km/h and then reoccur at 120km/h and disappear at 130km/h.
You can of course have a combination of both run-out and tyre in-balance. If the run-out is small then most people will have a balance done and possible won't notice the run-out cause they don't go that fast to really have a problem with it. Thus most people only think of balance as a problem.
What's also important is that if everyone went around checking their tyres for run-out quite a few manufacturers would be forced to lift their production and quality control standards because ...no one would buy them.