As far as I can tell, the concept (which I don't agree with, mind you) is specifically in regard to anything deemed sexual, because sex is magically different from every other thing that a human can do with their body.

Of course, what gets considered "sex" or "sexual" is quite arbitrary... and gets changed depending on what is most likely to result in the desired outcome in a given situation -- i.e. "some body parts were visible to a person below AoC" may be considered sexual in order to put a supposed "bad guy" behind bars, where in other situations that wouldn't be considered "sexual" (or "sexual enough")

What boggles my mind is hearing folks who argue in one breath for reform of laws around sex work, insisting that the "work" portion is the relevant part, and that sex is just one thing among many that a person can do... and in the next breath insisting that it's impossible for anyone below a particular local AoC to consent to sex, because sex is its own unique category, and it's not the same thing as asking a minor "would you like to go to Disneyland this summer? If you don't want to go there, we could also take a road trip and visit the in-laws..."

It's also an easier way for people to avoid self-examination around a topic they're uncomfortable with. If they insist that "children are incapable of content (regarding sex)" then they don't have to ask the question you did -- "Why? How is that so?" and can simply dismiss anyone else asking that question as one of those perverts who obviously doesn't want what's best for our children... won't somebody please think of the children?!?

tl;dr -- you're right that those who regurgitate the line don't understand "incapable" and "consent", and that's because they're afraid they might actually think about it and maybe even change their minds.