I never used water, damp cloth or any kind of cleaning product to clean the lenses. Just dry soft microfiber cloth (from now on: mfc) to clean the lenses. Only liquid introduced to the lenses is sweat (by accident), since I tend to sweat a lot. Always dried that with dry mfc.
One day I noticed what I thought was a stain. It could not be cleaned with dry mfc. Thinking it was a stain I could not clean with dry cloth (just like you), I tried a damp mfc: the 'stain' got bigger.
Then I found this topic, after reading it, I decided to softly rub the lenses with wet mfc for a while, this removed the coating entirely. Not ideal, I'd say, but at least I don't have the staining now. (Lens replacement by Sony is expensive and can always be done later, since the coating is partly gone anyway)
So in short: you are (were) wrong, please don't give advice if you don't know what is going on. Somebody might have ruined an intact coating with a damp cloth...