My opinion... "Delete that sucker!" If the information was on the cache listing and the cacher did not follow said information, they do not deserve the find. I believe this would also be covered by the "not within the stated requirements." portion of posting guidelines.
Now with that said, I agree that the CO may face retaliation from the person that had their log deleted. But the fact is we need to make a stand or our sport will go away.
There is a cache in our area that is placed on property clearly marked with "NO TRESPASSING" signs. From what I've learned, the signs were not there when the cache was placed, and the CO hadn't requested or received permission to place it there. When we rolled up on GZ and saw the signs, we passed on the hunt. I added a note to the cache listing stating that it was "posted" and gave my opinion. The troubling part is that people are still logging it and happily explaining how they just ignored the signs.
We depend on a whole lot of other people and places to be able to hide caches and hunt them. Taking no action against people who can't follow the rules (or CO requests) means that we encourage those people and it will only get worse. Eventually property owners and then parks, cities, and maybe even whole states will outlaw Geocaching altogether. I don't think that is an outcome that any of us want.
Keep in mind the the big "Switch" flips both directions, off and on.