I believe it. I had a home lab when I was a child. The Web didn't exist yet, but I read the scientific publications that were available at the library. It used to be common enough that there were books published about how to set up a lab and do research at home, like there were about setting up a home dark room for photography. (More recently I met someone who even had his own NMR (second hand, non-superconducting, but still) at home, was doing sophomore ochem lab activities at home at age 13, and left for university by age 15.)

It takes a child of remarkable interests and aptitude to win a national competition, of course. That's why you're reading about her specifically. It also takes unusually supportive parents. A sizable minority of American families with children could afford a home lab, equipment, and supplies if a child were so inclined and the parents encouraged it, but I suspect it's rarer for parents to OK funding it than other costly-but-more-common extracurricular activities or adult hobbies. Half of the battle is just having parents who understand you well enough to support what you want to do.