What would happen if an uninformed seller shipped a few cardboard backed sheets in a FC large envelope? Would the USPS intercept it and charge the recipient postage due? How would this rigid large envelope get handled vs a package?
If what you wrote is true, then you understand that the difference between and envelope and package is the thickness, specifically over 1/4 " is a package. Now there are sellers who purposely make the mailing more than 1/4 " thick in order to receive the tracking offered on 1st Class Packages.
Additionally 1st Class letters (up to 3.5 oz) and 1st Class Large envelope which do not meet the machinable standards are charged a "non-machinable" surcharge to avoid the machines and must be so marked.
As to where inappropriately paid matter is marked up for postage due, it is likely the clerk accepting the mailing or the employee making the final delivery to you street or PO Box. In the mail stream, it is unlikely to be noticed unless it sticks out like a sort thumb. Two such example who be a rustic metal post card dropped into a drop box and a legal sized envelope address and stamped not in the normal "long way" but such that the top and bottom edges are the narrow ones.