Did you consider making it an actual quiz with options to verify if someone actually knows what they claim? (Only skimmed the article, sorry if you mentioned it)
At the end of the day, your personal result will be for however you interpreted the instructions. But population-wide results should remain comparatively valid assuming each population is comparable in terms of being conservative/liberal with what they claim to know. E.g. you can still measure the difference between 25-year-olds and 30-year-olds because they're answering it in the same way collectively, and it's the differences I'm more interested in for research, than the absolute values.
I thought about making it something like a multiple-choice quiz, but it would have made the quiz a lot slower, and therefore either a lot longer or a lot less accurate, so checkboxes seemed like the only way to go.
I thought the explanations in the "more info" box was very useful. I'd suggest keeping it open by default on the first page (closed on other pages) as it seems a critical to read that box before taking the quiz. Just a thought!
So I would say no.