It's worth reading the other report [1] the article cites — it's a lot more comprehensive than the author makes it out to be. The study didn't find a relationship between Uber and alcohol-involved accidents/fatalities (which the NPR article is about), but did find a statistically significant relationship between Uber, traffic fatalities, and DUIs. They also found that introducing Uber increases auto-theft.

Using a differences-in-differences specification, we find that fatal accident rates generally decline after the introduction of Uber. Specifically, in the unweighted regressions, we find that entry is associated with a 6 percent decline in the fatal accident rate. Fatal night-time crashes experience a slightly larger decline of 18 percent. In both the weighted and unweighted estimations, we also discover a continued decline in the overall fatal crash rate and the rate of vehicular fatalities for the months following the introduction of Uber. For each additional year of operation, Uber’s continued presence is associated with a 16.6 percent decline in vehicular fatalities.

...

Again employing a differences-in-differences specification, typically with county specific trends, we find a large and robust decline in the arrest rate for DUIs. Depending upon specification, DUIs are 15 to 62 percent lower after the entry of Uber. The average annual rate of decline after the introduction of Uber is 51.3 percent per year for DUIs.

[1] http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2783797