I was only confused because you keep referring to being denied entry, but it seems what is actually happening is not being allowed to board.My PR card was stolen. I tried to use my American Passport to get on a plane, and one of the exceptions for Americans. The CBSA and the airline denied me, because the presumption is that a PR without a PR card is not a PR.
I am in the same situation now as I wait for a new PR card. I've waited for months. Without a PR card or PRTD, they may deny me entry to Canada, even though Americans have exceptions to the ban. The logic, such as it is, is that they won't treat me as a PR because I don't have a PR card, but won't treat me as an American because they know I am a PR.
They may have the same effect (if the only way to travel is by plane) but they're distinct procedures and concepts.
At any rate as the question above was originally about travelling from overseas. To which the answer is - yes, a PR needs pr card or prtd to board a flight to Canada and will be denied boarding without this (but entry at a land border is a different matter).
(Although this thread has meandered so if I've missed something, that's my oversight)