A fair point. That is why my proposal does not include any automated mechanism to delete logs or any similar measure. Just notify the cache owner so that he or she may take whatever action they feel appropriate. While your example is clearly an example of a case where such a tool would report a "false negative" (that a person does not qualify, even if they do according to the rules), it seems to me a corner case, although I have no data to back that claim up.
I would still argue that a tool to sort positives (people that _do_ formally qualify to log a cache and has adequately documented so) from negatives (people who, for whatever reason do not meet the formal requirements, be it erronous or not) would still have value as a challenge cache owner. If the log sheet is generally kept "orderly", most people will notice that there is a pattern to it. It only takes a couple to obfuscate the pattern. This tool would be a help a challenge cache owener keep the logs "clean" of obvious indifference to the rules.
Yes, there will always be black sheep. There are also people who cheat at all sorts of other aspects of life, including sports, love, business. It is not unique to geocaching. But there is a difference between covert and overt cheating. If you don't even try to create the illusion that you are in compliance with the rules (by for instance picking a number of caches that would make you qualify for that challenge and then couch-cache them), you are not even cheating - you are then simply too lazy to even try. Such behavior displayed overtly in the log will instill indifference in ordinary people, leaving the impression that following the rules are optional. If we accept this, then we better acknowledge that we are in scenario #2 of my original post - just don't give a damn, let anybody do whatever they want.
Imagine if everyone felt that way. That laws weren't worth enforcing if we didn't get 100% of the perpetrators. IMO rules are still worth trying to enforce, even if a 100% success rate cannot ever be guaranteed.