Many studies agree that parental involvement can either promote or retard cognitive (mental) development, and thus also affect student achievement. Bempechat (1992) cited Coleman et al. (1996) who reported that achievement was more influenced by family background and environment than the quality of the school.
It's true that homeschooling in general includes more contact hours at home, but it doesn't mean that learning is solely done at home. In fact, a big part of homeschooling is experience-based (experiential) learning outside the usual four corners of traditional classrooms. The whole world can literally become the student's educational oyster.