Uber has at times been giving route previews which has differed from the renderings of Google Maps. It’s very likely that the route preview is based on OSM data.
The following is a screenshot from the Uber app that shows a simulated route as a blue line. (click on image for large version)
We can zoom in to a few points which can be used as anchors, as you can see the blue line is not following the underlying Google Maps rendering.
I placed the screenshot into JOSM using the Piclayer plug-in, aligned as best as I can, adjusted the transparency and used Mapnik as a base layer. You can see the same reference points circled below which seem to follow the path quite precisely.
In conclusion, there is a high probability that Uber, at least for certain functionalities, is relying on OSM data.
Full disclosure: I have in the past applied for work with Uber.