I think the discussion refers to the fact that the US doesn't have the concept of being 'in transit'; that is, changing planes in the country without 'entering' it. Most other countries do.

[Off-topic: This is much more of a problem for visa-countries, than for Canada/EU: A Chinese businesswoman would have to do all of the US immigration documentation, interviews, checks etc. just to change at LAX to go to a customer meeting in Canada. So there's a big market for (non-US) airlines that allow travelers to travel between Asia and Canada or C/S America without transiting the US.]

So flying from Canada to Rome via the US means that you have to enter the US (immigration, customs and full security check), even if you are only changing flights.
In the case of Canada, this will be in the US pre-clearance done in Canada, rather than the US. There may or may not be another security check in the US, since arrivals from Canada are treated as domestic flights ("pre-cleared").

In the US, there's no general requirement that you leave the sterile zone to transfer. However, at some airports there isn't a single connected sterile zone and the arriving and departing gates may be in different zones. International departures may or may not be in a separate zone, but they often have extra security checks at the gate, in any case.

International arrivals have to clear security to transfer in almost every country, regardless of whether the connection is domestic or international. (Intra-schengen is not considered international in this context.)

Hope this helps.