We now await someone to come in here and say our Kirk violated the Prime Directive in sparing the Halkans and trying to affect change in the Mirror Universe.
On the contrary, I'd like to present this dialogue from "Ensign Ro" (TNG):
PICARD: Then I don't understand why you are unwilling?
KEEVE: Because you are innocent bystanders. You were innocent bystanders for decades as the Cardassians took our homes, as they violated and tortured our people in the most hideous ways imaginable, as we were forced to flee.
PICARD: We were saddened by those events but they occurred within the designated borders of the Cardassian Empire.
KEEVE: And the Federation is pledged not to interfere in the internal affairs of others. How convenient that must be for you, to turn a deaf ear to those who suffer behind a line on a map.
PICARD: Well, I'm not here to debate Federation policy with you, but I can offer you assistance.
Assuming this aready was Federation policy in the 23rd Century, I'd say that everything that happened in the alternate universe of "Mirror, Mirror" was "the internal affair of others".