I suspect what you say is true, this is a 'black mark'. Working for Uber? Maybe if you are in upper management, would it be a similar "black mark" but even then, are you going to blame every C_O for their scandals? Probably not all. As for the 98% of employees? I doubt working for Uber will seriously impact their next job (and much less all following jobs).
Just think, today we don't hold it against middle management or individual contributors who happened to be employed at Enron at the wrong time...