I would tell her because 1) I would want to know and 2) I don’t have friends that are too fragile to hear the truth.
None of my friends are purse aficionados and I think they’d be ticked that I (the one who has the most purse knowledge) would let them run around bragging about a fake purse being a limited edition. It’s not as if she even carried it quietly. She’s proudly sharing false information thinking it’s true.
Friends are the ones who should tell you things like you have bad breath, spinach in your teeth or visible panty lines. They “cover” you.

So, I’d fully expect my friends to set me right if I was ill informed in one of their pet categories and a little irritated if I found out later they didn’t.