I'm making an educated guess, here, but I have a strong suspicion that homeschoolers relate better to their siblings than do siblings who don't spend many hours every day together, i.e, public school students. This logic doesn't require much of leap. My experience with the topic (my credential, if you will), is based on my role as the mother of three homeschoolers, on my experience as a sibling, as well as on my observations of siblings, homeschooled and schooled, within my family's social circle and community.
My three daughters, for example, are observably more closely bonded than my sisters and I were as young children. The outwardly observable behaviors that suggest this strongly attached relationship between my daughters include the following.
Expressions of affection;
Offers of help;
Invitations to join in play or other activities;
Sharing interests;
Quick reconciliation;
Spontaneous apologies;
Overall positive demeanor when together.
My daughters play roles in one another's lives, such as teacher and guide, that non-homeschooled siblings are less likely to play. My younger daughters hold their older sister as valuable in this way. The older two act as assistant caregivers to their youngest sister. She looks up to them for feeding, play, and other help. Each child values her siblings for the ways she helps them and interacts with them throughout the days.
I ran and hid from my little sister. I preferred other friends and did not wish to include her. Her mimicking behaviors annoyed me. We hit and shouted at one another on a daily basis. I avoided her at school. Even as we grew older, my sister and I did not have much time to talk together. We had different friends, different activities, and little opportunity to find common ground. The difference in our grade levels at school kept us separate even in the same school complex. I often went entire days without seeing her.
I hear non-homeschooling parents complain about sibling rivalry, but I cannot relate to the situations they describe, except from my own childhood experiences.
Other sets of homeschooling siblings in our social circle and community appear generally happier. We see them together, enjoying activities together, holding hands, and talking about one another's interests and achievements with others. The fact that they spend time together in multi-age groups sets them apart from public school kids. They learn to relate to people of all ages. They learn to relate to people as individuals rather than to identify people based on grade level or age. Homeschool kids don't learn to avoid people, including their siblings, based on age or other school-based affiliation.
I could go on, but the gist of my observations is that homeschool siblings simply seem happier together.