But in that case, King had already shown an unwillingness to carry on governing when, as PM, he had requested a dissolution in order to avoid being defeated in Parliament on a motion of censure.  When Lord Byng refused King's request, the latter resigned, whereupon Byng commissioned Arthur Meighen to form an alternative government. Following the Meighen government's defeat on a confidence vote, Byng granted Meighen's request for a dissolution.  He could hardly have done otherwise. 

That situation is entirely different from the case of a new government losing a confidence vote within weeks of the previous election. If there be a viable alternative government that can be formed, it is incumbent on the Crown to explore the possibility. Cheffins is wrong to presume that a defeated premier is automatically entitled to a dissolution.