I think you probably "won", because the amount was not too large, etc...

Not exactly the same, but I had a situation where I could not recognize the amount and asked AMEX to fight it.
It was from some sort of shoe store in the countryside, on a Saturday.
Needless to say, I was convinced this was not from me.

They reversed the amount immediately.

A couple of days later, I received an email from a small software vendor who asked me what I didn't like about the software.
It turns out, they were the ones who charged me that amount...
Needless to say, I was quite ashamed on myself and offered to tell AMEX about my mistake but they never reversed the charges, apparently.

What I learned however was that AMEX sided with me without even consulting that vendor.
In a way, it's great but also frightening, especially if I am the vendor.

Maybe the small amount justified that action from AMEX.