Because both are representations of the rule and self-determination of the people. Popular uprisings are comparable to direct voting in terms of expressing the power of the people (though of course have other major differences in terms of violence, rule of law, etc).

> Because both are representations of the rule and self-determination of the people.

No, not really. Having a radical group remove another totalitarian ruler doesn't automatically grant them legitimacy or any arguments involving "self determination of people".