my two pennies...
First of all, if you are feeling a vibration and you found a loose lug nut, I would call them and have either the car towed to their shop to check things over or have one of the techs come out with the proper tools to check it (house call if you will).
Second, there is much argument of this, but...in most vehicles today, the wheels are hub centric...meaning that there is a 'lip' on the hub that the wheel centers on. The lug nuts provide the necessary 'clamping' force to keep the wheel against the hub and the hub 'lip' helps support the weight onto the wheel...but there are many 'opinions' on this.
Third, yes, because of lack of 'good' labor, it is possible for wheels to loose balance quickly if the wheel weight is not probably secure and they are 'thrown' off. I've had that happen just recently on my Sorento.
Fourth, not sure if was mentioned...but what kind of tires did you get? I've heard of 'cheap' tires that could not be balanced because of defects in the tires belt...the balance keeps changing...kind of like running Fix-a-Flat in your tire.
Lastly, maybe the loose lug nut was just a coincident...although a worrisome incident. Other things could cause intermittent vibrations...bad suspension parts, bad CV axles (not necessarily leaking), etc. Just something to ponder...