Cleaning mud, literal mud, off flood-damaged coins is perfectly OK. If the mud has been sitting on the coins too long and reacted with the metal, causing tarnish, then you've got two choices: leave it alone, or give it a dip in tarnish remover. Either way, your coin has lost value and it will be impossible to restore that value, since the damage has been done. Try to avoid polishing cloths, or other treatments that give a coin an un-natural "cleaned" look.
As for your specific suggestions...
Quote:
...avoiding use of tap water...
Tap water contains chlorine, and chlorine can cause "bronze disease" on copper coins. If you're soaking coins for a long time to remove mud etc then use distilled or deionized, or at least boiled, water to remove the chlorine.
Quote:
...not rubbing with a cloth...
Just like "Don't clean coins", this is a generalized statement aimed at beginners, to avoid having to ask and answer a whole bunch of ancillary questions. What kind of cloth? One of those fluffy soft microfibre things, or a piece of denim torn off some old jeans? You want to avoid anything that can cause unnecessary abrasion of the metal. "Polishing cloths" actually have grit embedded in the cloth to do the polishing; it's like sandpaper. You don't want that happening to your coins! Second, what, exactly, are you trying to rub off? If it's literal mud, that could have all kind of sand grains etc in it; rub away on a muddy coin and all those little grains will scour tracks in the coin's surface. If, on the other hand, it's something like PVC goo, you won't have the sand abrasion problem - but if you're not careful, all rubbing will do is spread the PVC goo all over the coin's surface, causing even more headaches later.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis