The reason that MRC01 has not responded is because there are no "regulatory definitions" of the words avoid and prohibited. This is not a case of "what the meaning of the word is is." These conventional words and their meanings, as used in an AFM/POH, can be found in a dictionary of American English. Some time ago, the aviation industry went through a re-write due to new standards adopted by the FAA and other agencies. Will was out; shall was in. An emphasis was placed on using simple, standard English. At no time before or since has the aviation industry employed unique "regulatory" definitions of the words avoid and prohibited. If MRC01, or anyone else, knows differently, and can cite an authoritative source, please enlighten me.
When dinosaurs roamed the Earth and I was teaching people to fly 172s, there were many hypotheses floating around regarding the slipping-with-flaps prohibition/admonition. I won't recount them because they were then, as now, hearsay. However, one explanation given for the substitution of avoid for prohibited has nothing to do with any design changes made to the airframe--it was suggested that Cessna, as the aircraft manufacturer, has no legal authority to actually prohibit us from anything, and therefore the language in the POH was changed. That, too, may be uninformed conjecture and I only mention it to suggest that, in the absence of fact, there are any number of hypotheses that can be associated with this issue, including the OP's assertion that "slipping with full flaps extended in our C172 is perfectly fine." If our goal is to operate as safely as possible, do we adhere to the guidance provided in The Book, or do we select from one of the many alternative facts available on the Internet and elsewhere?
And that brings us back to the OP: Are his/her students in jeopardy of getting pinked if they slip a 172 with full flaps during a checkride? Is the CFI irresponsible for teaching that the guidance provided in the POH may be cavalierly disregarded based on the advice of a non-authorative source? The answers to these questions do not pivot around definitions of terms, but instead, I suggest that they are matters that fall into the category of risk management and hazardous attitudes, as used in the ACS.