That's it, exactly, and congratulations. You're one of the very few people I've ever seen who seems to get that. Controlling dissidents or unruly mobs that are not armed is one thing; armed combat against their own countrymen is another matter altogether, and a standing army of professional soldiers is far more likely to refuse such an order. Governments understand this, too. That's a big reason why China used troops from the rural provinces to put down the Tiananmen Square insurrection in 1989; PLA units stationed in Beijing were thought to be too sympathetic to the urban students, and it was feared that if ordered to move against the protesters, they might switch sides. So they brought in units from the country who largely resented the students to begin with. And that was in totalitarian Red China - asking American troops to actually wage war on American citizens is a psychological barrier few generals would be eager to test.
