The Canadian "Starr Gennett" label belonged to the Canadian Phonograph Supply Company in London, Ontario, est. 1917 to import matrices from the Starr and Gennett labels in Richmond, Indiana. In early 1918, this company changed its name to Starr Company of Canada, but it remained independent of the American Starr Piano Co.
When the American company discontinued its Starr label in 1925, the Starr Company of Canada also stopped producing records.
The Starr label, however, was bought by the Compo Company, Ltd. in 1925 and continued in Canada until 1953.
So "Starr Gennett" [Canada] and "Starr" [Canada] were actually produced by two different companies, which, in my view, means we should not link them.
More info: http://www.capsnews.org/
I also don't see why we need to link Superior to Gennett; otherwise, we would also have to link Victor's budget label Bluebird to Victor and Harmony to Columbia, etc., etc.