This is absolutely correct. Plus, what they did may not be illegal per se, but we might not want them in the country. For example, I'm not aware of any U.S. law that specifically makes it illegal to have been Nazi concentration camp guard. But we don't want people like that in the country and want to deport them if they are ever found here. Hence the purpose of the immigration form.
Maybe not guards but that's splitting hairs. Nazi party members with rocketry experience were absolutely granted citizenship. Even von Braun himself used slave labor to build rockets during the war.
