I have observed this first hand. My first two roosters often lied about finding food, and the girls learned to ignore them. In fact, Panic Pants lied about food so often and so loudly that they actually learned to ignore him entirely-- even when he spotted danger. Not good! (I heard from his new owner recently by the way-- the older, bigger, sassy hens have him kept in line and he's been a good match for them, thank goodness)
For a long time, Lorp was the "guard chicken" and she was immensely observant to dangers. The other girls did listen to her.
Trousers doesn't lie about food, but the girls were used to fibs, so it took them a while to realize that he actually has goodies for them. Trousers is such a relief in my and their lives! It's amazing to see the dynamic when the hens aren't afraid of the rooster.
WOW, what a great read! Thanks for posting this info.....those sneaky roos!