Nobody doubts that Franklin used Peel Sound. The evidence is 99.9 per cent -- and certainly solid enough to convince Roald Amundsen and every serious researcher since.
The simple fact that Franklin reached the northern coast of King William Island exposes this “undiscovered Franklin Strait” argument as specious. It's a red herring designed to confuse the uninitiated.
Lucky or not, Amundsen established the first navigable Northwest Passage.
He sailed Lancaster Sound, Peel Sound, Rae Strait, and west along the coast. 
Of these waterways, Rae Strait was the last discovered . . . the final link.
Ergo, John Rae discovered the final link in the first navigable Northwest Passage. 
Re: all white males are interchangeable: Rae was objecting to his mapping being credited to the Royal Navy. 
As for giving the Inuit their due in the context of reviewing Dead Reckoning, Kenn Harper shows the way:
http://kenmcgoogan.blogspot.ca/2017/10/arctic-expert-kenn-harper-sings-unsung.html
Ken McGoogan