I've been in the position of the other mum, only with a cousin.
I know cousin struggled with friendships at school, and I suspect probably would get an autism diagnosis nowadays. I've had several times when they've related something to me and I could tell that they hadn't got the real meaning behind what was said.
Anyway their dd was silly in a similar way at that age. Cousin smiled proudly and said wasn't it lovely that they could be themselves and children nowadays were so tolerant of different people, and she was so confident with others.
I kept quiet, but I could see that when we went out, although cousin would tell me how her dd made friends with everyone because she would go up to anyone, that other children were actively avoiding her. Cousin was telling me that they were playing nicely and it was all down to how sociable her dd was.
When she was 12/13 I took her out with my ds and she started doing this to him. He asked her several times to stop it, and she replied, "I can't help it, I'm just built to talk about it all the time". He replied "in that case I'm going to play on my phone because I don't want to talk about that."
Interestingly immediately she stopped and for the rest of the day was very sensible and lovely.
Now fast forward to now. She's nearly in her 20s. She still does it. Cousin can't understand why she doesn't have friends. Her dd struggles with feeling left out, but cousin tells her to be herself and real friends like you for who you are.
That's true. Real friends do like you for who you are. But when what you want to do makes other people uncomfortable, you're unlikely to make friends who are going to see past that.
I did once try to say to cousin that sometimes you need to try fit in to make friends. She was not impressed.
Sometimes I wonder whether I should have tried to say more. I'm not certain it would have worked, and I know cousin would have gone up the wall. But I do wonder whether her dd would be happier if someone had tried to help her to see what was unhelpful when trying to make friends.
So what I'm saying is that it's possible the other mother was being nasty. But, maybe she was trying to give a head's up to the Op. It's hard to hear these things about our dc, but sometimes being given an insight how others see us/our dc can help us guide them to make choices over behaviour etc that will make things easier for them in later life. And we'd all like an easy life, wouldn't we?