A little over a year before Bozoma Saint John became the first chief brand officer at Uber, the transportation company’s best hope to rehabilitate its tarnished image, she hailed a ride from the Four Seasons hotel in Austin, Tex., to a nearby business dinner. What pulled up was a wreck.

“Hey, nothing’s going to happen to me in this car, right?” Ms. Saint John said half-jokingly to the driver. “You can drive, right?”

She expected him to banter back. Instead, he told her that a group of taxi drivers at the airport had vandalized the vehicle and that he needed the money from this ride to fix it. He also mentioned that he had been saving to see Iggy Pop, his late brother’s favorite rocker, at the South by Southwest festival, which Ms. Saint John was attending as the head of global consumer marketing for iTunes and Apple Music.

She gasped. Her dinner was with Iggy Pop. Would the driver, perhaps, like to come along?

Cue the tears (and the five-star passenger rating).