In order to obtain a PPL in a glider, one only needs to be 16, which is younger than the age to get a driver's license in many states. For airplane and heli, it's 17, and there's no evidence that every 17-year-old has such a license. So there doesn't seem to be any correlation between an actual drivers license and a pilots license, so long as the reasons for not having one aren't in violation of any other laws, regs, or decrees to which you're subject. You must still provide appropriate identification.
The two applicable FARs regarding disqualified for non-FAA-related legal or regulatory actions are 61.15/.16, which refer to alcohol and drugs, and 61.18, which refers to security disqualification. 15 and 16 don't apply, as you wrote.
61.18, however, has to do with security threats. If the Transportation Security Administration (TSA) has notified the FAA in writing that you pose a security threat, then you would also be disqualified.
If none of these apply, then you (or perhaps better, an aviation lawyer) can write the FAA's chief counsel and ask for an opinion. The relevant contacts are here