Actually, there are moonquakes, but they're caused by tidal forces rather than plate tectonics.
Like most totalitarian governments, Aegis Overlord is deeply into propaganda and image management. Their duplicity has been implied before: the Aegis ambassador in GH1 who thinks that Pirate Point is representative of the entire planet, and the ambassador in GH2 who will "correct" any misinformation the player may have heard.
Of course, the message broadcast on Luna and the message transmitted to other worlds need not be the same. The Aegis Doctrine is "Strength through Unity"; this translates into a strong central government, a nationalistic population, and no toleration for deviance. Originally the colonies which would become Aegis Overlord continued to refer to themselves as Pax Europa. When it became clear that Pax Europa was destroyed and was never coming back, a new mythology of trans-Lunar nationalism was created. According to this mythology the Lunar colonies represent the only unbroken line of civilization from Earth's past onwards into the future. It is therefore vital that Luna be kept safe, and also vital that it become powerful enough to help restore the rest of humanity to a civilized state.
As Aegis expanded, this myth of trans-Lunar nationalism was used to help integrate the conquered domes. A common tactic for expansion would be to instigate conflict with a small colony (or between two unaligned colonies), then use the conflict as justification for invading somewhere else. Eventually the non-Aegis domes formed an alliance and began to fight back effectively. The stalemate lasted for several years until the beginning of the unification war.
Tycho Madang was destroyed as a demonstration of Aegis's new weapon systems, particularly the Chimentero. Within the Aegis-aligned colonies, it was reported that a lunar quake had ruptured the dome. This was obviously due to sub-standard non-Aegis construction. The ADF offered assistance to Tycho Madang but was turned back by the dome's militia. When the seriousness of the situation became apparent, the ADF commander ordered his troops to disperse the militia and take the dome so they could offer aid to the survivors. Consequently, all surviving members of the Tycho Madang militia are now outlaws on Luna. Aegis propagandists used this story to show the danger of resisting the Aegis Doctrine. Clearly, if Tycho Madang had accepted Aegis's help, tragedy could have been avoided.
Most residents of the already-integrated domes took this story at face value. It helped Aegis to convince them that war was needed to unify the planet. Residents of the non-aligned domes typically didn't believe the story... in their case, it led many domes to surrender rather than risk depressurization.
Rumors that Tycho Madang had been destroyed by Aegis forces were squelched when several high-profile citizens of the dome stepped forward to confirm the Aegis version of events. The leader of the militia actually came forward, confessed to blocking aid from the Aegis Defense Force, and allowed himself to be arrested + executed*. On Luna itself, this pretty much ended the debate.
Mischa grew up in one of the original Pax Europa domes. She didn't hear the theory that the ADF had destroyed Tycho Madang until several years after the event. She dismissed it as Earth propaganda. Although she knows that Aegis isn't really to be trusted and that the state media often lies, she's like anybody and doesn't have a flawless BS filter. By the time she heard the truth the Aegis version of events had already set in her mind.
So, "blatantly use force and never apologize or conceal" is certainly part of the image Aegis tries to cultivate, but part of the reason for that is so they have plausible deniability when they do decide to conceal.
*Could have been brainwashed, could have been blackmailed, could have been a copyclone or robot duplicate.
