Your credit card company is the entity you can expect to apply basic logic.

In the short term, that logic will be to refund your money to keep your annual spend, but not to bother Uber. In the long term, this could raise the fees Uber pays for credit card services.

Long before Uber, a JAX airport auto rental was improperly tacking an $8 fee onto every "paid in full" Hotwire reservation. This can add up over a year. When challenged, they lied and claimed it was an upgrade. American Express of course made no effort to protest this, they just refunded my $8. Not very satisfying, but still my best course of action.