Dave S,
It is not the orientation of marks that seems to be the unassailable principle, but the orientation of the golf ball (as John Morrisett indicated earlier); i.e., being able to orient the golf ball however you want.
Location of marks trumps orientation of marks only in determining what was "already there"; i.e., what can indicate the line of putting to the player without penalty.
So you're saying that re-orienting the mud clot in your example would result in the green being touched and therefore a violation of 8-2(b)? OK, let's go with that.
So it now appears that a player can:
(a) use whatever is "already there" as an indicator of the line of putting. Anything that was already located where it was--the coin on the green, the old ball mark, the mud clot, and apparently the line on the golf ball that was already on the golf ball. How any of these marks are oriented has nothing to do with whether it was "already there" or not, whether the mud clot or the line on the ball.
(b) orient the golf ball however he wants as long the ball is replaced and not moved.
I can find no counterexamples to (a), i.e. something that was "already there" that a player cannot use to indicate the line for putting. (Sounds like you think the mud clot might be one if you just re-orient it, but the violation would be because the green is touched, not because it still indicates the line for putting.)
I can find no counterexamples to (b), i.e. any rules situation that does not allow the player to orient the ball however he wants as long the ball is replaced not moved. Not even the mud tee.
And it appears as if a player/partner/caddie can not:
(a) introduce something that wasn't "already there" to indicate the line for putting. That's putting the club down, touching the line, water bottle on the fringe, caddie intentionally standing somewhere or casting his shadow, etc.
(b) re-orient a mark that is "already there" (the mark would still be "already there", and it could still be used to indicate the line for putting, but the putting green would be touched which would be the violation).
The only counterexample to (a) (because Rule 1-1 handles the player and the putter) could be if a player puts a new line on an unmarked ball after it has come to rest on the green. This could be "placing a mark to indicate the line for putting" and therefore a violation (I don't know), but the Rules could also say that the principle of being able to put an ID mark on the ball when lifted overrides the restriction on placing the mark to indicate the line for putting.
The only counterexample to (b) could be re-orienting a mark that's off the green, but again we're getting into another absurd situation--one of the 0.01% of the situations the rules wouldn't easily handle (again, I've never seen anyone do it).
It feels like we're getting close to tidying this one up unless you can find some counterexamples I can't.