Earlier quoted context omitted.
I wouldn't even attempt to contact Uber in this situation - a fraudulent charge on a credit or debit card = call card issuer or bank. I don't care what the company is, I call card issuer.
unfortunately, most banks have the policy of first asking you to resolve it (or at least show evidence that you've tried). I would say, sending uber an email would work, or calling their number (which, they actually do - if you lost a phone in an uber, they have a number which lets you call them to get the contact details of the driver of the car you were in).
So it only applies to chargebacks of transactions you've previously authorized, not for fraudulent unauthorized charges.
If I took an Uber (or attempted to take an Uber) and I had a dispute with them about payment = attempt to work it out with Uber first.
If I didn't take an Uber at all = contact bank.