My girlfriend isn't on my policy because she never drives my truck. Likewise the vast majority of the time I drive her car it's something along the lines of repositioning vehicles in the driveway. If I were to get in an accident in her car chances are there'd be a bunch of fighting with insurance but our insurance (same company, different policies) would probably wind up paying. Would I count as an uninsured motorist in that hypothetical situation? III has a very obvious incentive to portray insurance as something worth having as opposed to a waste of money (which it will be for most people who don't get into a situation involving medical or large amounts of property damage). I think they'd consider me uninsured in that situation.
Reporting rates also have an effect. There's a much higher reporting rate for small accidents with a single uninsured party than for similar accidents in which both parties are insured. If one party is insured it's in that parties interest to maximize documentation unless it's undeniably their fault. If both parties are insured then it's much murkier, damage amount, deductibles, who's at fault, etc, etc. come into play and if the dollar amount is relatively low it's often more faster and cheaper for them to settle the matter without insurance company involvement. Basically, if someone without insurance gets in a parking lot accident the vast majority of people will report it whereas that's not necessarily the case when both parties are insured.
This holds for my outdated one in seven number and the new 12.6% that GP linked.
That sounds like it comes from the same people who make any speeding offense on par with DUI and having an at fault accident in most points based systems. One in seven people with a license not having insurance I can see (because they might not have a vehicle) but one in seven vehicle/driver pairs on the road not being insured for that combination seems very high without monkeying around with the statistics.