OVERVIEW: Yes, it is correct that PRs who are American citizens can board a flight to Canada from abroad without presenting or possessing a valid PR card. In contrast, PRs who are citizens of other countries must present a valid PR card, or a PR Travel Document, to be given a seat on an airline headed to Canada from abroad.
PRs do NOT need a valid PR card to actually enter Canada. Does not matter what their citizenship is.
Note: I will probably skip citations to authority or sources below. This is a subject others here and I have discussed at length, in-depth, in numerous topics here, where I and others have referenced, cited, and linked both official and other authoritative sources. If you are skeptical or otherwise looking for confirmation, you should be able to use the site's search function to find at least posts by me "dpenabill" that include these sources.
LONGER EXPLANATION:
For clarity: Whether a Canadian PR needs a valid PR card, and when, depends on context. For purposes of keeping PR status, there is no requirement to have a valid PR card, so PRs are not required to apply for or obtain a replacement PR card when their card expires.
However, a valid PR card can be required in some circumstances. In situations where a valid PR card is required, generally (that is in most contexts with some specific exceptions, regarding which I will get to below), the PR's citizenship does not affect whether a valid PR card is required. The PR's citizenship makes no difference, for example, when a PR applies for coverage by provincial health care insurance. Some provinces, like B.C., require presentation of a valid PR card, while others like Ontario may accept an expired PR card (for up to a certain amount of time). No special or separate treatment for American citizens.
I recognize that your question and comment are undoubtedly in regards to PR cards and a more limited context: traveling to and entering Canada from abroad. So . . .
TRAVEL to versus ENTERING Canada:
There is a big difference in what is needed to ENTER Canada VERSUS what is needed to board an airline flight headed to Canada from abroad. That is, TRAVEL to Canada, and that is travel with COMMERCIAL carriers in particular, is subject to more strict requirements than who border officials will allow into Canada, including who border officials MUST allow into Canada.
PRs MUST be allowed to enter Canada.
In particular, in this context it needs to be recognized, with some emphasis, that there is NO requirement a PR have a valid PR card in order to be granted permission to physically enter Canada. Here too, the PR's citizenship makes no difference. Easy to forecast it is likely to be easier, in the Port-of-Entry (PoE) screening process, for an American citizen than it might be for PRs from various other parts of the world. But generally a person who is a Canadian PR MUST be allowed to enter Canada when they arrive at a PoE even though they do not present or have a valid PR card. The only question is whether or not they can sufficiently establish their identity (valid passport from any country would usually suffice) and PR status, and for most PRs establishing their identity will suffice in establishing PR status (the latter accomplished by border officials verifying the traveler's status in their GCMS client records). Typically it goes much easier if the PR can present direct documentation of their PR status (expired PR card works best; copy of CoPR works) or at least corroborating identification (provincial drivers' license for example), but no particular documentation is necessary as long as there is sufficient information to verify the traveler's identity and correspondingly their PR status in the system.
This is mandated by statute. It is not a Charter right. So it is a little different for Canadians who are PRs, who are statutorily entitled to enter Canada, versus Canadians who are citizens who have a Charter right entitling them to enter Canada.
Note: Canadian PRs are NOT Foreign Nationals in Canadian immigration law.
In reference to an American citizen you say that "as a visitor they can enter Canada with a US Passport - but not as a permanent resident."
Canadians in Canada are Canadians. Including Canadian PRs.
Be they Canadian PRs or Canadian citizens, if and when they enter Canada lawfully (that is properly going through a PoE) they are in Canada as a Canadian. Regardless what documentation they presented at the PoE. Even if a border official is not aware they are a Canadian and waived them into Canada as if they are a Foreign National visitor, thinking or mistaken they are a FN. The latter has no effect on their status. Those who are Canadians PRs are in Canada as a Canadian PR.
This is why some PRs abroad in breach of the PR Residency Obligation and without a valid PR card, who have status allowing them to travel via the U.S., will try to return to Canada without applying for a PR TD, by traveling to a U.S./Canada border crossing, presenting a visa exempt passport to Canadian border officials hoping the border officials do not question them about being a PR and their compliance with the PR RO . . . hoping to be waived through without being reported. If they succeed, and are waived into Canada as if they are a FN visitor, they are still PRs and can legally stay and work and so on, and as long as they wait long enough their days in Canada meet the RO, they can then apply for a new PR card without risk of losing their PR status.
There are other risks doing that. These days most will be readily recognized as a Canadian PR because their GCMS client record will pop up on the screening officer's computer. Worst case scenario then is being Reported for a PR RO breach. They will be, as they must be, still allowed to enter Canada . . . but if Reported they will need to appeal to keep their PR status.
If they make misrepresentations to the border officials, such as deliberately concealing the fact they are a PR, and get caught, that can lead to admissibility proceedings and potentially the loss of PR status. But pending any such proceedings they will be, as the must be, allowed to enter Canada.
PR card Requirement to "Travel" to Canada:
The need to present a PR card (or a PR TD) ONLY applies to travel on commercial carriers. This applies to almost all but not all PRs. (Similarly true for Canadian citizens, who must present either a Canadian passport or a special travel document to board a commercial flight to Canada from abroad.) This is implemented and enforced through the regulation of commercial carriers, specifically in regards to who commercial carriers can provide transportation to Canada.
There is an exception for U.S. citizens. That is, the regulations requiring Canadians to present certain documents to show their Canadian status do not apply to travelers carrying a U.S. passport. So American citizens who are also a Canadian (either a PR or citizen) do NOT need to present documentation to show their status in Canada. Thus, in particular, PRs who are American citizens can board a flight to Canada from abroad without needing to show either a PR card or a PR TD.
That is how it is. Might not make sense to some, but it is mostly about how these rules and regulations fit into the bigger scheme of reciprocal, mutually accommodating provisions for citizens in the two respective countries. It is part of the same regulatory scheme that requires most visa-exempt FNs to have eTA in order to board a commercial flight to Canada, but similarly not American citizens.