Ambiguous ownership when discussing multiple character body parts
I think you have already nailed it in the question itself, only that you are underestimating the function served by the emphasizing word own there— It disambiguates the two sentences and leaves no doubt as to who is placing whose hand on whose shoulder.
Often, standalone sentences like yours might leave doubt as to the implied meaning, but contextualizing them should remove any sliver of doubt. Thus if this scene was part of, say some storyline, it should be readily apparent to the reader as to who is the sympathizer and who is the one sympathized.