"But she said..."

This is one of the things that I still don't understand in this country, and I came across one yesterday.

My wee one went for swimming with her friend yesterday afternoon. After saying goodbye to her friend and coming home, she asked if she was allowed to play with the friend after tea. I told her "No", because there's tons of housework to be done in  and around this house, and I desperately needed a hand or two.

After teatime, her friend called. I opened the front door, and told her that my wee one was not playing with anyone. Then, we exchanged these words:

Girl: "But she said that she was allowed."
Me: "Allowed? When did I allow? I didn't allow her such a thing."
Girl: "But she said that she was allowed."
Me: "But she is not allowed, and I never told anyone that she could go out after teatime today."
Girl: "But she said that she was allowed."
Me: "It doesn't matter what you think. I am the one who decides, and she is not coming out today!"

My wee one must have replied "Yes" at swimming pool when she was asked by the girl if she could play after teatime. But how dare the girl keep repeating as if I was a liar or being unfair for changing my mind! I don't understand why she pushed her luck in that manner. Well, she once told her whole class that she had been to Japan when the truth was that she had never got out of N Ireland. (Probably she was jealous because my wee one went to Japan.)

She reminded me of one of my in-laws who always insisted things even when they were obviously untrue. She was always like:
"But I saw this" (But there was no way to prove that she had actually witnessed it.)
"I can bring my friend, and she will tell you the same" (Would the friend travel all over to my house and tell me that my in-law was a bloody liar? Of course the friend would be behind her no matter what the truth was. Also, another witness could not have proved anything still.)

I know that this is a small community where any gossips can be regarded as truths (wherever in the world, people believe what they want to believe, after all) and also where quite many number of people don't question and analyze anything scientifically because they were brought up hearing "Because the Bible says so". But why do some people talk that sort of nonsense to me? Maybe they think that I'm stupid and gullible.