Now, the way I think it works is that keys 1-4 are assigned by default to multiplayer chat options, and since multiplayer is very very unused in FSO for a long time now (hopefully that will change... soon), many mod makers opted to use the keys for special abilities, selecting stuff in mission and things like that. And the builtin script that detects the key press, looks for the keys on their function basis, not the physical key itself. And since your (Multiplayer) Message keys are not bound, it can't find them.
So my suggestion, just bind the 4 multiplayer chat options to 1-4, but use [Alt], [Shift] or [Alt]+[Shift] with these. That should clear any conflicts and let you use the keys.