1. Same geocoded file is being used for Origins and Destinations.
2. We've compared SourceID, SourceOID, PosAlong, and SideOfEdge from the Origins file to those in the Destinations file. SourceID, SourceOID, and SideOfEdge values are exactly the same. PosAlong is different for some of the cases. However, a > 0 distance is being calculated for approximately 5% of the cases where all four variables are exactly the same. Most of these distances are close to 0 (about 90%) but 10% are greater than 0 when rounded to hundredths of a mile. Several are over 3 miles for the same origin and destination...
3. We are not sure why PosAlong for some cases is different when the source of the Origins and Destinations file is the same.
There can be many reasons why non-zero distances can get computed for same location. it may have to do with the curb-approach and u-turn policy set in your analysis in conjunction with one way restrictions, etc. Or it could happen if your network dataset has multiple line feature sources and the the locations may get snapped to a different sourceid. But in your case the SourceId is the same so it could be the former. So I would suggest that you copy a pair of problem locations to a route analysis layer and run a shortest path and see what is the resulting shape that gets generated to get some clue on what may be causnig the non-zero distances.