Firstly, @JBH should be applauded for not only raising this issue, but for providing a detailed account of his reasons for voting to close this question. I say this, despite disagreeing with those reasons, because it sets an admirably high standard for making decisions about questions on this site and in meeting the criteria for peer review. We need more like it.
JBH wrote his reasons in the following comment.
As written, the question is off-topic because it is about the plot of your story, not world-building. In other words, how to conspire to cover-up the incursion is not a function of the rules of your world.
Now my response to this was in part about how the OP's world differed from our own reality. This is not my substantial argument, although it does in part refer to one of the ways worldbuilding functions. Namely, to build worlds that differ in some degree from quotidian reality. The brevity and insubstantial nature of my argument was due to the restricts on word count allowed in comments.
What can be argued is that the question is about elements of worldbuilding and isn't about creating the plot of a story or, as seems to be the case here, a game.
Let's take the relevant criteria for the FAQ and see how they apply or not.
Creation of elements of a world (languages, species, buildings, etc.)
Effectively this is the contemporary world, with added supernatural monsters. The created element here is the monsters.
Effects of events or world elements, including biology, technology and magic, on specific aspects of that world's societies, cultures, and environment
The OP has a situation where a township is besieged by supernatural monsters. How the question isn't how will institutions like the police and civil authority respond to a plague of monsters, it is about how the most reasonable action they can take, namely, calling in Federal authorities like the Army, Navy, Air Force and US Marine Corps, FEMA or the Boy Scouts. Hereafter, all forms of outside support will be referred to as the "US Cavalry".
How to achieve a specified effect in a defined world, including by the use of biology, technology or magic, while maintaning [sic] in-universe consistency
Now achieving a specified effect in the OP's defined world is precisely what the OP's question is asking. This also means it is a worldbuilding element within the criteria of the FAQ. While establishing may or may not include the use of biology, technology or magic, there will always other factors that could achieve this effect. They can be social, political, cultural and environmental.
Now let's look at the criteria for exclusion.
Actions of individual characters, rather than elements of the world they inhabit
The actions required by the OP's question are not those of individuals they are instead the actions of institutions, and although WB's criteria doesn't label its various social and cultural aspects of worldbuilding as "institutions" that's exactly what they are. The US Cavalry etc. are institutions. Therefore, their actions cannot be those of individual characters.
Obviously not. Let's move on.
Elements of plot
I am sorely tempted to rant about poorly understood plot is by many of this site, but my long involvement as a writer, an editor of an anthology, as a literary critic, as a writers' workshop teacher, and as the coordinator of several writers' groups shows eve writers have problems understanding the nature of plot. It would be accurate to say the question does not involve elements of plot and simply leave it at that, but that would be too easy.
Plot is anything that drives a story forward and shapes the nature of its resolution. By the way, don't worry if you don't fully understand what that means. You won't be alone. This also means that almost invariably when the criteria concerning story-based are applied here they are applied in error. As is the case here.
So far this answer has demonstrated that the criteria in WB's FAQ either do not apply as presented for the reasons for closure and that the question properly meets the criterion as a worldbuilding element.
In his post above, @JBH presents the following reasoning.
In the balance, I still feel the question is off-topic because the world (despite having some differences with the real world) has police, military, and political leaders who want to cover up something. That's no different than the real world and, frankly, monsters create no different reaction than would any other real-world problem the police, military, and political leaders want to cover up.
As I said above the rationale for worldbuilding where the world in question only differs slightly from reality as we know it isn't the strongest rationale for worldbuilding. (Aside: Worlds that differ slightly from reality can be among the challenging exercises in worldbuilding. The most insignificant false step can bring the entire edifice down. The wider the divergence from the quotidian and the more latitude the worldbuilder enjoys.) If JBH is arguing that the OP's world is exactly like ours, then I am puzzled. Because that would constitute a legitimate answer to the question. However, it does contain a serious flaw.
Yes cover-ups do happen in the real world. Yet it is possible to see why a cover-up couldn't or wouldn't happen with an incursion of supernatural monsters. The cover-ups that occur have certain characteristics in common. They are usually contained. This can be geographically, or only happen in the main to disadvantaged groups of people socially, economically or politically. If they were exposed the events would cause institutional harm or have direct negative impact on figures in authority.
Remember the key aspect of the supernatural monsters was they were causing terrorist-scale criminal activities. Now this the complete opposite of why the US Cavalry's covers things up. There is a mountain of political capital to be gained by going into battle with monster from another world. Any cover-up, especially if the facts leaked out, would be massively counterproductive.
Surely, some adviser would be whispering, for example, do you want to be the POTUS who allowed the monsters to gain a foothold on the planet? Or do you want to be elected POTUS for life by a grateful nation?
In summary, the question in question does not meet the criteria for its closure and it does meet the criteria for being on-topic as worldbuilding.