Here is what would provide for a way stronger claim:
1. Aggregate DUI levels change since UBER started operating across all cities with no UBER service.
2. Aggregate same data for cities with UBER.
If UBER causes decline in DUI rates hypothesis is true, we can expect two trends:
1. On average cities with UBER will observe relative number of DUI's going down when compared to cities without UBER.
2. Amount of UBER rides given will be positively correlated with decrease of DUI rates.
Personally I think it would make sense that UBER decreased amount of DUIs and I would really like a data released that can prove it.