Dietrich Gruen started long friendship with Leo Abey at German Grossmann school and work at German Assmann watch business. Swiss Aeby was earliest movement supplier to Gruen at Columbus from his Madretsch location 1875-83. My example here is an 1879 that is very like a model 1874 Waltham. NAWCC photo. Aeby's own movements at the time were typical good Swiss undecorated so my suspicion is Gruen liked the Waltham design and referred it to Aeby.
Also he spent quite a long time working with Dietrich learning American production methods and machinery. Thus the reasons Assmann and Aeby&Landry were primary early movement sources
for the Gruen watches 1895-1920. Info gained from personal observation, actual watches, advertising, catalogs, and 3 well written hearsay histories. Possibly factual; at least partially. Fun to conjecture.