B.N. Morris open gunwale canoes have had a rail cap-- all of them do unless somebody removed it and didn't replace it... I believe Morris devised it as a segue from the deck to the open wale... to ease the eye into the open wale which wasn't initially accepted by the public. Morris may have begun building canoes this way in 1905.
My experience looking at Morris canoes-- either the real thing in-person or in pictures-- is that if you have an oval serial number plate on the gunwale or a rectangular plate on the bow stem, you have a Morris. If there was a plate saying "Kennebec", then you'd have a Kennebec, but to my knowledge no such animal has been found and this is what Benson suggested, and is what we're looking into.
If a Kennebec canoe has a short, heart-shaped deck, it is a second-grade canoe and will not be trimmed in mahogany-- at least this is my memory from studying catalogs. This rail cap was used by Kennebec from 1910 and it became one identifying factor for the Kennebec. Morris didn't make very many open gunwale canoes and was out of business by 1920, so that particular look in a canoe seems "wrong" for a Morris, yet that's the way they looked-- there just aren't many of them out there.
The first grade mahogany-trimmed Kennebecs were long-deck canoes. There are other differences between Morris and Kennebec-- Is the canoe in question mahogany trimmed? Is the keel fixed with a screw on every rib? Is the profile of the canoe a Morris profile or is it one of the Kennebec models?
I'll give you links to the videos I made on how to ID a Morris and one showing a Kennebec/Morris hybrid compared to a Morris, and this may help. The other big-identifier would be the pocketed ribs, but they aren't there with the open gunwales... so look at the canoe's profile and some of these other aspects. It might help to have some who have restored both Morris and Kennebec to add some differences they've noticed in basic construction.
http://www.youtube.com/watch?v=yU2iyygvr8I (Morris Kennebec)
http://www.youtube.com/watch?v=uAz-rspieqE (Morris ID 1)
http://www.youtube.com/watch?v=YN462MWTABc (Morris ID 2)