The tl;dr is that GET/DELETE/PUT are idempotent, whereas POST is not. The author suggests that POST should be used on "collection-like" resources, e.g. '/Persons' to create a new Person while PUT to update/create a specific Person (i.e. you know the identifier of the Person in the system). Multiple PUTs on that resource, with the same payload body, will not change the state of system.
This makes sense, and, as far as I have seen, is the "normal" way to approach REST (for various definitions of REST). What puzzles me is that the first referenced article ("How to Create a REST Protocol") actually doesn't advocate the PUT=CREATE mapping. Maybe I am missing something?
Reaching the article's concluding paragraph, the author states: "PUT must create or update a specified resource by sending the full content of that same resource". OK, but this complicates matters, since the client now needs to know how to address a particular resource i.e. have implementation/domain-specific knowledge.
My approach is using POST to create, and PUT to update (NOT create/update). I find that it simplifies things quite a bit.