If it's possible to trick the FMS as it seems they are not denying. Then in bad weather the pilot could easily be given false information to say that he's flying straight and level when he's actually in a dive or inverted. If you depend on your instruments and they are giving you bad data then in the right conditions it could certainly cause a crash. There have been planes that have gone down over the ocean because they could not tell the difference between the water and the sky and they did not trust their instruments and are in an inverted dive when they think they are climbing. Imagine if their instruments said they we're climbing and they thought they we climbing but were really in an inverted dive!
The FMS does not override those types of sensors. It is more about signaling the path of other aircraft. Broadcast a false danger and a pilot/autopilot will alter the course.