Flaps,
I thought you handled the situation very well. You didn't berate her infront of the rest of the crew, you also tried to offer her some constructive feedback.
Did she tell you that she had had a problem with pilots before- had she encounted one of the few 'assholes' in the company and was scared for life. Or was she easily impressionable and therefore had taken to heart the bitching of another crew members feelings towards pilots.
At seven months in a company I am suprised that she fought you so hard on this issue- however you had obviously developed such a raport with your crew that they felt comfortable enough to stand up if they felt strongly about something (however misguided ). Great for CRM.
At my airline the cabin crew are encouraged to interact with the flight crew as much as possible to break down any barriers. We are constantly reminded that they are also part of the team especially when dealing with emergency situations. Does your airline have this type of culture? I also encourage my crew to visit the flight deck as much as possible- even going out of my way to get them to feed and water the pilots and collect their rubbish. Even 30 seconds worth of communication is better than none.
Perhaps 'forcing' her to spend a small amount of time in the flight deck on quiet sectors could show her that pilots are people too.
Maybe send her into the flight deck with a purpose such as learning how to use their radio to contact the ground, or get their perspective in an emergency situation.
Hope this helps.
love SMILE