They know that it may entail a physical search if there is a question about some item in their bag, or if the X-Ray operator cannot see through an item to determine if it is masking something else.

That is what constitutes a “reasonable” search on the checkpoint.

It may end up going so far as to open seams of a bag if it is determined that there is an unidentified item artfully concealed in the bags seam.

I have never personally seen this happen, but the rules we operate by leave that as an option.

You have used the term “administrative search” several times, but its not a very descriptive term. Could you please explain your understanding of the term?

Administrative search
Definition
: an inspection or search carried out under a regulatory or statutory scheme esp. in public or commercial premises and usu. to enforce compliance with regulations or laws pertaining to health, safety, or security <one of the fundamental principles of administrative searches is that the government may not use an administrative inspection scheme as a pretext to search for evidence of criminal violations People v. Madison, 520 N.E.2d 374 (1988)>
see also probable cause at cause
The U.S. Supreme Court held in Camara v. Municipal Court, 387 U.S. 523 (1967), that a reasonable administrative search may be conducted upon a showing of probable cause which is less stringent than that required for a search incident to a criminal investigation. The Court stated that the reasonableness of the search can only be determined by «balancing the need to search against the invasion which the search entails." Cases following Camara have stated that the probable cause requirement is fulfilled by showing that the search meets reasonable administrative standards established in a nonarbitrary regulatory scheme.