however are you telling me that if a pitot tube of some other probe (a la AF447) freeze up or just fails to function properly the FCC will still take its inputs and get confused instead of disregarding them and work in a "less than ideal" situation?
As usual : it depends.
Normally a system should detect that the available data is corrupted/invalid/senseless/outside the norm, and hence should not get confused, but take the action it is designed for. Which might be switching off and leave it to the pilot to solve the issue. All input to systems should come from independent and redundant sources (e.g. 3 pitots feeding three air data computers), If one delivers data which is different from the other two, the system should understand that this one is at fault, and use the data from the others. If all three differ, the system should understand that no valid data exists, and act accordingly.
However, being designed by humans there might always be situations nobody ever thought of, and hence did not design the system for. This is valid for any complex product of any manufacturer.
See the Spanair accident in Madrid, where the very old fashioned pre-computer-systems got confused, and did not warn the pilot when having full authority to do something wrong.
Sometimes protections kill you, sometimes the lack of protections does. Sometimes systems safe the day. Some days they fail. Most important is that the pilot fully understands the systems in his aircraft and works with them, not against. A pilot which is not trusting his systems should not fly that aircraft.