Because they're not going to waste that kind of effort on their foot soldiers. The planners, yes.

You're doing the same thing 1pg did and assuming that every terrorist is the same. They're not. They will have some dudes who will have a plan. They will have other dudes who all they know is they need to be someplace to meet a guy and that's it.

But this is someone they believe will have the capability to successfully fool multiple Homeland Security officials in multiple interviews that they are from a different country, have experienced repression or persecution that they haven't experienced, and can persuade those officials to release them from detention despite having no documentation and being unknown to all their fellow travelers.

Right.

If these guys are just foot soldiers, they're not going to be able to pretend (in flawless Honduran-inflected Spanish) to be from some Central Triangle country fleeing persecution sufficient to fool a DHS officer who spends his day literally doing nothing but talking to people fleeing the Central Triangle. The amount of training necessary to pull that off would be insane (to say nothing of the fact that terrorist organizations that we're really worried about are unlikely to have many assets in that part of the world to provide the basis for that kind of training). It's just absurd.

Anyone who's got the skills to pull that off is worth buying a fake passport for. Which, again, is what all the other international terrorists do and have done.