There have been a couple of recent threads over in the Robot Identification forum about evil robots who request every possible permutation of myadmin.php, optionally preceded by a request for /muieblackcat. The latter apparently means that one of the robot's friends has been there before.
After a while this led to the generic advice: if you don't actually have any php on your site, throw a quick [F] at anyone from anywhere who requests anything in \.php$. Problem solved.
Unless...
History:
I noticed that a couple of local .htaccess files for +Indexes had stopped working. My host was doing some work recently, so I checked with them first. Nope, 'tain't us, check those big complicated htaccess files at the top level.
Lovely. This is where g1 gets to gloat and say I told you not to combine mod_rewrite and mod_alias in a single .htaccess.
Well, maybe not. The culprit turned out to be the single line
RewriteRule \.php$ - [F]
Haven't heard back from the host yet, but I have to guess there is some kind of php involvement in those auto-generated indexes. (I'm hoping they come through with an ! escape clause so I can allow this php and none other. The logs don't give any useful hints.) So by blocking all php requests, I'd disabled the feature all the way up the line. A local +Indexes can override a global -Indexes, but it can't open a side door when the front door is locked.
Lesson:
You can unconditionally stop a whole class of malefactors at the gate, or you can have auto-indexes, but you can't have both. Drat.