I import NAD83 latitude/longitude data (EPSG 4269), and the coordinate values displayed are correct. I enable on-the-fly (OTF), then import Google Satellite data, which is automatically WGS84 Pseudo Mercator (EPSG 3857). The coordinate values are corrupted, but the vector overlay looks spatially correct on the Google map.
If I now assign the coordinate system back to NAD83 EPSG 4269, the coordinates for the vector layer are correct, but the Google layer has shifted and will not zoom correctly. I've tried all combinations of loading and assigning datums and all fail. It appears the problem is the Google Pseudo Mercator datum; I tried transforming the vector layer into WGS72 and NAD83 UTM Zone 11 and all was fine. It appears that once a Google layer is imported you are stuck with bad coordinates.
Note I have tried this on QGIS v1.8.0 and 2.14.0 and different operating systems.