It's not about whether the mistake is honest. I have no reason to believe this woman was being insincere or playing the racism card to get out of trouble. I think she genuinely believed she was being singled out because she's black. She was visibly upset about it.
And this is exactly what I find so tragic. Because it so obviously wasn't true.
Yes, black people are allowed to make mistakes and be vulnerable and be human. You do these things countless times every single day. I'm not trying to put you down because you're not acknowledging this, I'm trying to point out that refusing to acknowledge it, telling yourself this false story about the world, only hurts you. Racists, for the most part, are quite happy for you to mistakenly think you're the victim of racism.
As James Baldwin said, you have to let yourself believe that you have a place in the world. That you deserve to walk through the world as if you have a right to be here. He figured that out over sixty years ago. During segregation (although it's true he had to leave America in order to do it). For black people to truly thrive, some of us still need to figure it out today.