No, that is even more reason for Cliges to accept it!
And how devastating would it be if they were both spies, and both supported the mission? There is no way we could ferret them out before the 5th mission. They would both be on mission 4, sabotaging it, and then we would waste time debating which of the two was a Spy for mission 5. We would not figure it out. So if they were both spies, then Cliges would support it.
And besides, my point is that even if I am incorrect about Falc being a spy, then that doesn't change the fact that Cliges is a spy; and Cliges did not support it. Ergo, the spies did not want that team to proceed. Ergo, we should propose that team again.