Seems like a pretty good fit. Khosrowshahi was brought in to take Expedia public and Expedia and Uber's business models are close-ish.
Expedia went public in 1999 [1], when Dara Khosrowshahi was working for an Expedia competitor: IAC. He didn't join Expedia until 2005, when IAC acquired Expedia [2].
Maybe I'm missing something?
[1]: http://www.nasdaq.com/markets/ipos/company/expedia-inc-1567-...