"Is the parcel in the geographical bounds of the city name entered?"

The "city name" on an address isn't really a "city". SFO's address is "San Francisco, CA", but is not within SF city limits.

Queens NY addresses have "cities" that are just neighborhoods.

Applying any kind of logic to addresses will just be a minefield.

The Pentagon's address even has the wrong state. The address is Washington, DC, but it's in Arlington, VA.

In much of unincorporated america, the most valid form of an address just uses the nearest city regardless of boundaries. Almost nowhere actually guarantees that every bit of land is even in a city limits. At the margins, addresses are unstructured free form text that is correct if it can be interpreted by a human with local knowledge.

There’s also no particular reason to expect that an address corresponds to exactly one parcel or that any given parcel has an address at all or that any given parcel has at most one address.

hundreds of people in my city-county really think they live in a city in the next county over just because of the "city" label on their zip code

Yeah, this is bizarre. I don't know how it works in Canada but in the US the city/zip of the mailing address is just the location of the post office that delivers mail. It has nothing to do with the municipal the address is actually in.