I may have misread but I believe in this case the OP didn't have her Green card with her. In that case she is under no obligation to arrange for the Green card to come to the POE just so she can show it to the officer.
A traveler's obligation, in a PoE examination, is to truthfully answer the questions asked, and CBSA also has the authority to inspect any and all items the traveler is bringing into Canada, including documents or devices containing highly sensitive, private information. This includes the contents of an individual's telephone or other electronic device (refusing to give passwords sufficient to facilitate access to information can result in the device being seized for further inspection . . . more than a few travelers have been tripped up when the information on their telephone was different than what the traveler has told the examining officer).
If CBSA wants to examine additional documentation or information, which is possible even though I have not seen instances of this reported, that would probably require a formal investigation which, of course, would have to be done according to the rules and law governing the government's access to an individual's property and information. What is more likely, I believe, is that the PoE officers make a referral to a local IRCC office or to the RCMP for the purpose of investigating whatever it is that concerns the PoE officers.
It is common for IRCC to request PRs to submit copies, or present originals for inspection, of documents like Green Cards, drivers licenses in other jurisdictions, records of movement from other jurisdictions, in addition to any and all travel documents issued by other jurisdictions, in the course of conducting a Residency Determination. No crime is committed if the PR fails to provide a copy of a U.S. GC, but of course that failure can be considered in IRCC's assessment of the PR's credibility and have a negative impact on inferences made.
If she has it in her possession at that time then of course it is a different case.
Definitely. The officers at a PoE have authority to inspect anything and everything a traveler is bringing into Canada.
Caution: Being
cute, such as giving an item to someone else to bring into Canada for you, may work one or four times. Overall, however, pursuing game-playing of this sort tends to ultimately work to one's disadvantage. CBSA and IRCC personnel have, so the saying goes, seen a thing or two. They figure things out far more than many realize.
I still don't understand how despite being present within that country's territory half the usual rights don't apply. That's a different issue though.
Not sure what you mean by this. Not sure what "rights" you are referring to.
As for a traveler's rights at a PoE, they are very limited. In this regard, it is worth remembering that unless and until a traveler has been admitted into Canada, the traveler is NOT in Canada while in the PoE even though that is on Canadian soil.
(Persons who circumvent border controls in order to get into Canada without being admitted, and who are subsequently interdicted by authorities, are in Canada -- these days there is, for example, a stream of persons coming into Canada seeking asylum who are crossing the border illegally, and Canadian authorities are actually waiting for them, arresting them, and these individuals then can make a claim for asylum from WITHIN Canada -- these individuals deliberately cross at a location where they will be arrested, so as to begin this process.)
Border control laws give CBSA officers authorization to inspect EVERYTHING being brought into Canada. There is virtually no limitation on the scope of this authority. It must be reasonable, but what is reasonable in this context is extremely broad. And, even if it is not reasonable, the traveler rarely has any remedy. As noted before, the officer who acts unreasonably, or even that officer's superior who in effect allows an officer to act unreasonably, could face discipline.
It may be worth noting that a Canadian citizen has a Charter Right to enter Canada. A PR only has a statutory right (sometimes called a "privilege") to enter Canada. FNs have a statutory right to fair procedure at a PoE but no explicit right at all to enter Canada. No one, however, has a right to enter Canada without first applying for permission to actually enter Canada (this application is in effect made by arriving at a PoE and seeking entry), and persons applying for permission to actually enter Canada must agree (which agreement is implicit in the act of seeking entry) to be examined and subject to inspection, including the inspection of any and all items the traveler is bringing into Canada.
For the vast majority the vast majority of the time, the border crossing transaction is perfunctory. Sometimes it goes differently.
