Here was the idea: 1) Combine Fremont buildings layer (pretty detailed) with MS buildings (poor details, but no substantial biases). Then, for a centroid of each F-building, find the offset to a corresponding centroid of an MS-building. Finally, look at the distribution of such offsets for the nearest 50-100 F-buildings and take the median as an estimate of the offset by which a given F-building should be moved before importing it into OSM

Here is the result (red polygons are the original ones, blue – after the adjustment using the MS building footprint layer): https://drive.google.com/file/d/1IeNMu8r6iHjvmt7yOxO06Uggra8sI4os/view?usp=sharing

Looks pretty good to me! :)