I think you're exaggerating their limited participation. But I don't blame you, the parents themselves probably believe that they play much less active role than they really do, simply because they don't keep track of everything they do to help their kids learn. And just to be clear, I'm not talking specifically about reading. I'm talking about their entire education (including mathematics, science, history, etc.). The younger the kids are, the more guidance they need, whether direct or indirect.
If we focus exclusively on reading, creating environment that encourages kids to try is more than enough. When there's plenty to read around the house and kids see their parents reading often for themselves (not just reading to the kids), the "monkey see, monkey do" principle will drive them crazy about reading. I know because I was like that as a 5-year-old.
But let's go back to education in general. I started teaching myself programming when I was 10 years old. Now I have a degree in Computer Science. So I can see in hindsight how much time I wasted learning useless crap simply because I didn't know better. I also felt for a long time that I was missing something important - it turned out to be the whole theory of algorithms, complexity and proving correctness that I've later learned at university. If I had a mentor early on who would point me in the right direction every once in a while, I could have learned much faster and avoided some bad habits that I still struggle with today.
I also have another personal experience with learning on my own: English is my second language. I had to take 11 years of compulsory English classes (since 5th grade all the way up to second year at university). I got my first computer after the first year of English. Another year or so later, the classes became complete waste of my time because I was learning much more from computer games. I've also learned some key insights that I'm successfully using to learn a third language at the moment.