Now why would she think that is what sending the troops would mean?

Well two possibilities there ,
1 you are quoting out of context
2 she hasn't read the authorisation for shooting in self defense
Neither of which alter the fact that your statement .....It is a type 5 mandate, no shooting allowed under that type, unless they are under emergency of being destroyed, and Hezbollah rockets miss 95% of the time, hence they can not respond to them. That is the reason the French Defence Minister gave for only sending 200 troops, so take it up with her if you don't believe it.
....is bollox , a statement that you posted to attempt to clarify this......The ceasefire only authorizes the peace keepers to fire on Israelis, not Hezbollah, even if Hezbollah rockets hit them.
....which is complete bollox .