The only time I had heard the "no water" addage, was in relation to copper & brass relics. It turns them a sort of orange tinge, that's not appealing.
As Tom said, the “no water” mantra mostly applies to copper/brass/bronze coins and relics. It seems somewhat counterintuitive considering those coins have been sitting underground getting soaked in rain and maybe snow melt for decades, but rinsing old copper coins in water really does seem to hurt the appearance of the coin, depending on the overall age and condition. Overall, water is actually a very efficient cleaner - in my engineering days, we referred to it as “the universal solvent”. For some older, worn coins, rinsing or scrubbing with water actually removes too much dirt. Sometimes leaving a little residual dirt in the crevices helps the detail stand out a little better.
Here’s an excellent video by YouTube personality “Aquachigger”, which vividly demonstrates why you might want to avoid using water on older copper coins:
Don't carry anything in the field to clean! Take your time at home, if something is actually valuable you'll destroy it wiping in the field.
I used to completely agree with this, and I still don’t clean anything in the field....except silver coins. I changed my mind on field cleaning silver coins about a year and a half ago, after ruining my oldest silver coin find, an 1854 seated quarter. After I dug it, the obverse of the coin was completely covered in a thin layer of soil - since I never field cleaned at that point, I put it in my “specials” pouch to clean later at home. Well, when I got home, I accidentally brushed the face of the coin across the lip of the pouch ever so slightly when I took it out to clean it at the sink. And that’s all it took - the rough sandy soil clinging to the obverse dragged just enough to leave 3 small but obvious parallel scratches across the face of the coin.
Anyway, from that point forward, I’ve been bringing a small spray bottle in the field with me. I immediately spray all the dirt off my dug silver right at the hole before going into a cotton lined pill bottle. I haven’t noticeably damaged a silver coin since.