So glad that I found this thread. There was a guy who did almost the same thing, plus more, at my old office in DC. He was an older gentleman who worked on a floor with mostly younger folks. We were a digital agency that shared a floor with some small boutique futures company (or something like that). They had about 3 women and 2 men. He was one of those men. He had severe OCD, but I do not think this was not about keeping the latch clean.
This was his routine (which he did no matter what, even if someone was in the bathroom with him):
1. Walk into bathroom and immediately wash his hands.
2. Grab about 10 paper towels.
3. Get a few of them wet and soapy.
4. Go into stall and presumably wash off the seat and dry it.
5. Place numerous seat protectors on the seat (not just 1 or 2, like 5 or so).
6. Take dump.
7. Never flush. Never.
8. Leave protectors on seat.
9. Emerge with a paper towel in his hand.
10. Use it to turn on sink.
11. Wash hands.
12. Grab about 10 more paper towels.
13. Use one to turn off sink.
14. Use one to mark the stall door such as your culprit.
15. Use one to open door and then proceed to throw it on floor inside bathroom as the door is shutting.
Now, it might seem odd that I know all of this, but it was a constant source of entertainment and discussion in our office. The guy was infamous. We shared stories about him all the time. The women in our office always wanted to hear the story.
The strangest part was that he didn't seem to mind that we saw all of this. He didn't alter his behavior if we were in the bathroom, even the non-flushing part. It was almost like he hated the younger folks and wanted them to stay clear of his territory.
We surmised that he would leave without flushing to deter others from using the toilet. He marked the stall to remember which on he had used (maybe) b/c there were 8 and it was never the same one.
People are strange.