Eva's cover story is paper thin

[Dirty Duck]

Snake and Zero discuss the fact they don't know if they can trust EVA and that she is definitely using Snake for her own gain, but they simply have no choice but to trust her. It's not like they can pull the plug and abandon the mission as then both Snake and Zero will go to jail and FOX will be disbanded. And in the end EVA was the only reason Operation Snake Eater's public purpose could be achieved.

Whether Zero knew about EVA's cover story falling through, we don't really know.

The entire operation was hastily cobbled together and everyone involved's last hope, as well as a desperate plea to appease the Soviets and prevent a nuclear war. Who the person who showed up to help them among Volgin's ranks actually was and why was kind of less of a priority.