Sure they will. That's been standard doctrine for decades.
I feel just the way your daughter does about telling the truth, so although I accepted everything "mother" taught <eye-roll>, I never assumed a "theocratic" right to lie to people except in matters of life and death.
To give them their due, all the examples of "theocratic disinformation warfare" I saw in the literature were life-and-death situations: David fleeing for his life, Nazi Germany, etc.
g ently f eral