When a node (501609671) associated with a way (41113036) is moved, the way appears in Overpass's augmented diff output as though it changed (which its geometry did), e.g.

<action type="modify">
<old>
  <way id="41113036" version="1" timestamp="2009-09-19T10:30:53Z" changeset="2532203" uid="110076" us
    <bounds minlat="41.8432372" minlon="12.6208508" maxlat="41.8432812" maxlon="12.6210011"/>
    <nd ref="501609670" lat="41.8432812" lon="12.6210011"/>
    <nd ref="501609671" lat="41.8432372" lon="12.6208508"/>
    <tag k="highway" v="service"/>
  </way>
</old>
<new>
  <way id="41113036" version="1" timestamp="2009-09-19T10:30:53Z" changeset="2532203" uid="110076" us
    <bounds minlat="41.8432288" minlon="12.6208433" maxlat="41.8432812" maxlon="12.6210011"/>
    <nd ref="501609670" lat="41.8432812" lon="12.6210011"/>
    <nd ref="501609671" lat="41.8432288" lon="12.6208433"/>
    <tag k="highway" v="service"/>
  </way>
</new>
</action>

However, the only changeset visible in this fragment (2532203) is the changeset in which the way was originally created. As a result, osm-adiff-parser credits the original changeset (2532203) with the modification rather than the changeset which actually modified the geometry (54135745, per http://www.openstreetmap.org/node/501609671).

The clue here that the way shouldn't be credited to its original changeset is that version didn't change. Given that, it becomes necessary to look through the current augmented diff for entries corresponding to any of the referenced ways and use the associated changeset id as the target.

This is touched on indirectly by drolbr/Overpass-API#407. Addressing the problem upstream would likely involve including some indicator about which component was modified such as additional metadata for each nd ref (version, changeset, timestamp, etc.).