The supplemental info often mentions how there have been a mysterious string of disappearances where people with backgrounds in the military, science and engineering just vanish from their homes with no sign of struggle. They aren't being abducted by aliens, they're being recruited by XCOM and agreeing to the absolute secrecy requirements.
In Mente Materia it seems that the worst political pundit in the world managed to get the opportunity to confront XCOM for their unsanctioned military actions and covert alliance with an alien race. Considering the influence of the Council, that is implied to include at least the Vice-President of the United States, it's possible that they deliberately allowed the leak to reach Senator Coleman specifically, so that he would make any opposition of the XCOM project a joke in the eyes of the general public when it inevitably became public knowledge — someone more competent could have presented rational and crushing arguments against the organisation's existence in its current form and seriously hindered their current operation model.
After The Reveal in chapter 28, one has to wonder: just why have so few humans been able to access the Field to this point? Also, when Twilight describes the Field, she describes it as feeling like it hasn't been used in a long time... could it be that there were once more people who could use it? If so, where did they go? And why?
In-universe Fridge Horror as the XCOM researchers find out more and more about Equestria, and due to their invader-induced cynicism, put the absolute worst possible spin on it.
One researcher observes that cutie marks sound like the perfect method of social control. Want more soldiers? All the foals get combat-related cutie marks. Running low on crops? Increase the rate of farming marks.
Cadence's love powers look an awful lot like city-wide mind control to a suspicious psychologist.
Someone points out that given Celestia's demonstrated levels of power, if she ever finds Earth there is absolutely nothing XCOM could do to stop her tossing Earth into the sun. And considering that they're keeping her student prisoner, she'd have every motivation to do so.