What you're looking for is a study that shows something like the following: The difference in social development between at least 2 groups of children: Where one group did not socialize at all, and another that socialized with similar-aged peers.
Also, while the study you link is interesting, it's really just looking at pro and anti-social behavior over what seems to be one school year. It's not doing a formal assessment of social development over a long period of time. There's certainly evidence it could be beneficial long-term, but long term effects aren't studied in that paper.
I think your mistake is that this does not describe homeschooled children at all. They just socialize in locations other than prison-style government run daycare centers.
If RMS were a homeschooling advocate, this is the kind of statement I'd expect from him.
If you are on the "right" side, there's no need to exaggerate.
In what way is that statement an exaggeration?
Do I need to spell out how public schools are run like prisons? Or do you not believe in their critical function as daycare facilities?
I was curious about this, so I searched for developmental psychology on the difference between mixed-age and same-age socialization. But what I found (from a very brief search) didn't match what you said. An example study is this - Children’s Social Behavior in Relation to Participation in Mixed-Age or Same-Age Classrooms:
"Findings suggested a significant positive effect on children’s prosocial behavior as a result of participation in a mixed-age classroom context. In addition, fewer children appeared to experience social isolation in mixed-age classrooms than in same-age classrooms. Aggressive behaviors were significantly less likely to be noted by teachers in mixed-age than in same-age classrooms." - http://ecrp.uiuc.edu/v1n1/mcclellan.html
But that's just one study. Is it an area of ongoing debate in development psychology? What sources would you recommend for the other side?