New attempt at reformulating it so that Taco Lobster gets it!
For a given discard pile, you might have
A) Discarded things while only caring about what's on top of the pile
or
B) Discarded things while trying to put them in such a way as to manipulate future draws.
For any given shuffle, you might have
1) A good shuffle; things are mostly randomized.
or
2) A bad shuffle; patterns that were there in the discard persist after shuffling.
If you have (1) a good shuffle, then it doesn't matter whether you had (A) or (B). So why not just do (A)?
If you have (2) a bad shuffle, then (B) is deliberate cheating, AND will prevent you from recognizing that you had a bad shuffle, so the honest thing to do is (A).
To summarize:
1+A = OKAY!
2+A = OKAY! Or, at least, honest, though you should shuffle better.
1+B = OKAY!
2+B = NO! BAD! CHEATING!
Therefore, the honest thing to do is (A). Because IF you do (B), you're either doing something which has no effect (and why would anybody do that???) OR you're implying that you will do a bad shuffle, thus making this action matter.