Not the op, but it doesn't sound like you're trying very hard to understand. Simply put—and speaking as a person who doesn't care about what adults do and see on the internet involving other adults—there is simply no bulletproof way of reliably ensuring children do not see or experience something online that is inappropriate for their age (or against a parent's personal sensitivities), while preserving a parent's freedom to encounter such things. As one who ardently opposes censorship and supports accessibility to information and material that some may find objectionable, I can empathize and understand why there is a need in people's minds for wanting to have something that works flawlessly, without requiring them to lock down every device and constantly hover over the shoulders of their children when they are using internet-enabled devices. Some parents who feel this way can very well be consumers of material they think is inappropriate for their children, wishing to prevent their children from being exposed to such material until they deem their child has enough maturity to properly understand it and place it in a context for life, while also wanting to avoid being hovering, controlling parents who make their children feel like they're controlled and permitted no freedom to grow and learn and make mistakes.

For example, I'm a fan of Game of Thrones, but I wouldn't watch it with an 8-year-old. Extrapolate that to the realm of porn—especially of the BDSM or other such role-playing and kink variety—and we wind up in a place of genuine conflict for some parents, even those who might enjoy such things themselves. Moreover, there is more than a small amount of collected evidence and accounts from people who document how such material is impacting such things as teenagers' views on sexuality and what behaviors are normal, as well as young women encountering what they report as the effects of porn on their teen male peers—with such reports including expectations of sexual acts before they've even shared a kiss. The prevalence of such information and imagery, which the average adult may be able to successfully contextualize, provides a different set of challenges to the inexperienced and less mature adolescent population.

So, no, what the parent said wasn't that "information (and ergo imagery) is accessible" is the problem. It's more likely that the problem is there's no shortage of ways that people, young or otherwise, can stumble upon or be introduced to things that can be seriously problematic for their level of maturity and development.

Despite all that, just to be very clear, I'm not suggesting that government-issued porn IDs or similar programs are the answer, or that they would even help solve the problem some people legitimately worry about and feel matters for their, and their children's, lives. I see a lot of problems with even suggesting that, and think it's an awful solution. But I think there's value in recognizing there is a problem strongly felt by many people, and the problem isn't merely access to information and imagery. As with many things in life, I find myself mixed between recognizing the value in empathizing with and understanding people's concerns, and unapologetically upholding on principle the accessibility of information (and imagery) some may find objectionable.