This is about a Canadian case. There is no such thing as a precedent from an American court.

In theory, any ruling in any Common Law country could be cited as precedent in any other Common Law country.

As the US has the 4th amendment, most US search-and-seizure cases rest on it. If anyone were ever so bold as to argue a positive right to privacy for all humans--rather than the weaker but easier to prove prohibition against US governments committing privacy-violating acts--and the case was decided on it, that case could be used as precedent everywhere.

Judges are generally careful about not doing that, for obvious reasons. If a lawyer tried to make the case about a right to privacy, the judge might decide the outcome of the case base on that, but the opinion would certainly say that the litigant won or lost because of some other reason.

Statutory law is generally robust enough that judges can almost always decide based on it rather than on discovered law. So it's not that Canadian courts couldn't accept American precedent, it's just that American courts make special efforts to not set any Common Law precedent that a Canadian court can use. If it ever happens, it's likely to be in civil equity cases between two or more non-government parties.

Why do people feel a need to post laws and such which are not relevent to the discussion?

This is hosted on CBC (Canada broadcasting corp) and clearly this is about the "Canada Border Services Agency (CBSA)"

what does US laws have to do with this?

Sometimes when there is a lack of local jurisprudence, courts will look at other jurisdictions for guidance. But it’s more common for a colony to do that when the motherland has more case law.

In British practice my understanding is that it would be A v. R.; the website of the Supreme Court has judgements the form R. v. A and A v. Her Majesty The Queen. Whence your usage?