That’s a great question, Mike — and one that I’ve tried to keep in mind throughout this research (as with any survey research, you always have to think about whether the questions you’re asking are questions people can reliably answer).
I’m fairly confident that we’re not seeing a gap in parental accuracy/acuity here, mainly because I offered respondents an “I don’t know” option for each type of misdeed — and there’s no consistent pattern to which category of parent is most likely to say they don’t know whether their kid has engaged in a specific kind of misbehavior. If the issue were simply that limiters are in less denial about their kids’ misdeeds, I’d expect to see a higher proportion of “I don’t knows” among enablers and mentors, but that isn’t the case; in fact, it’s often (but not always) the limiters who are most likely to say that they don’t know whether their kids have engaged in a particular form of misbehavior. (But for most types of misdeed, the “ I don’t knows “ are in the ~5% range — occasionally breaking 10%).
With regard to your larger point — -about kids’ freedom today — I couldn’t agree more. It’s another reason for embracing technology, in my view: giving a kid a mobile phone is a great way to strike a balance between providing more independence and ensuring kids’ safety.