It sounds like Laura was from academic branch, where her parents were probably very engaged, and thought they could do a better job than the school system--which is great.
My parents, and most of their friends who homeschooled were from the religious branch of the movement, which is fairly large in the US. Their main motivation was to basically prevent the school system from teaching us things they didn't approve of, like evolution, etc. Of course, we learned about evolution, but from a very different (and very incorrect) perspective.
Regardless, we still took standardized tests, and performed really well on them every year. Overall I did fine in college--aside from a few academic blind spots, and I'm doing fine as a programmer today. The social stuff was a steep learning curve once I hit college, but I made it.
I will say there are a number of people I know who didn't "make it out". College can be a really big jump for a lot of these kids.
It's too bad there aren't more things like that.
It's not for everyone, but I've met a lot more homeschooled people since, and I've never met someone who's wished they hadn't been.
My parents' goal for our (me and my siblings') educations was basically just to teach us how to think. They cared a lot more about what we were like at 25 than what we'd be like at 15. I found this to be super freeing, and something I valued a lot.
We didn't have much money growing up, and my dad worked 3 jobs so that my mom could stay home and homeschool us. My mom was actually a public school teacher, and wrote a paper in college on why homeschooling should be illegal. I have always loved her willingness to change her mind on that once she realized that public school wasn't the best fit for us.
My parents both sort of split the "education" responsibilities, and they really tried to empower us to view learning as a journey we could join them on vs. something that was compulsively forced upon us. So, whenever possible we would learn things from the "real world" vs. a textbook or classroom setting. I remember when we were learning about the pulmonary system, my mom convinced a local butcher to give her some cow lungs so that she could show us how inflating / deflating lungs worked. When we learned about the founding of America, she put us in a van and drove from Florida to all 13 colonies and visited all the historical sites.
I found the transition to traditional school and then a big public university with 50k students to be quite easy. I also played a lot of sports growing up, and I find that sports / music / other forms of community tend to give kids plenty of socialization, and the "homeschoolers are socially awkward" meme is a bit of a myth in most cases.
Anyways, it was hugely positive for me. It's not for everyone, and requires a specific type of parent with a specific type of motivations, but I think it can be incredible for many families.
An extremely intelligent friend of mine is one of those people, and he has hang ups about it.
Note that there are good home schooling experiences as well, but there may be some selection bias regarding the stories we typically hear.
The worst outcome I've seen has been my sister, who is in her thirties and rarely leaves my father's house.