I think that in many cases, homeschooling can be of benefit to children, and my wife the elementary school teacher helps out a lot of our friends who do homeschooling to some degree or another. Having said that, anyone who works in pediatrics or law enforcement can describe cases of physical or mental child abuse that occurred under the guise of homeschooling as a way to keep the abuse from being discovered. I am not sure what the answer is.
I don't think anybody is trying argue in absolutes. Some kids are certainly abused at home, and the perps "homeschool" to keep it from being discovered. But that is a tiny fraction of homeschool kids. A more meaningful question would be, what percentage of kids are homeschooled to facilitate abuse vs the percentage of kids abused by teachers/administrators/other kids at school?
I know of 1 family that homeschooled largely because the dad was sexually abusive to 6 of the 7 kids (why not the 1, I have no idea). That man was still in prison last I heard, turned in by the pastor when the abuse came to light. The mom continued to homeschool afterwards, though with a lot of outside observation that she requested.
But I know of several families that homeschooled for at least a year or two if not longer, because of severe bullying their child was subjected to that the school refused to address. I don't personally know anyone who was willing to tell me they were abused directly by a teacher/administrator, but they're in the news too often.
And I know of MANY people abused by various adults in their life without legal consequences (even though reported in some cases) who went to public school the whole time.
In other words, homeschool vs public school is not really a factor in the odds of a child being abused. If it is a factor my money is on homeschool being safer overall. Abusers will find a way to abuse, no matter the schooling choices made available.