I really hate using this kind of cop out response, but it kind of both. The government did interfere on the private turf, but when human rights were being violated despite the "All men are created equal" stuff, the south really lost all right to complain. You see this a lot in history, where people conveniently forget parts of their own laws to their advantage, or root through to search for an old law that nobody enforces / find a loop hole. And when the South decided to succeed and attack the North, that didn't help their case much.
Sadly enough, Lincoln's reconstruction plan would have helped the south much more than the one given by congress to Johnson. Dealing in what ifs aren't really my thing, but if booth hadn't shot Lincoln, there probably wouldn't be such a division between north and south in the future years.