I was reading this post, and i think that the problem isn´t the secrecy of the Phalanx group, but the nature of the war. I think that the whole figthing must be secret to the public. What i mean? The aliens can come to Earth frecuently but don´t make a massive assault. Why? There´s many explanations, but i prefer to think that is a very bad cost/effective way to make the job. They simply can use a sickness to scrub the humanity, for example.
So, i think that the battle must be secret, the alien missions are "special operations" to achive the goal of the "sickness" (the game have a history of this) and PHALANX is a counter-alien special operations group. That´s all.
How to explain the attacks to population? That´s the point. If you fail a mission, people start to know the reallity of aliens and the nations start to have "media problems" and riots at the streets, so, the nations will cut your funds. But, if you have succeed, the "battle" can be covered and the life continue "normaly".
How to explain the fallen UFOS? well, military "secret" aircrafts
. The attacks on cities? Terrorist group (Like Cobra?
). Homemade videos of battles and aliens? Well, trivializing the video or hacking the Youtube
Some ideas...