Toothpaste is the most popular of the cleaners. However, depending on the mask it may work or not. The glass lens of some masks are hydrophobic. The reason for this is not clear but might have something to do with the process of manufacturing the glass. If it is a coating, it is not silicone because solvents known to cut silicone are ineffective in improving the glass' wetting ability. Without wetting, droplets will form; another name for droplets is fog. The two Promate/Swift frameless masks that I bought would not respond to any of numerous separate treatments using pastes, soaps, vinegar, alcohol and detergent. Toothpaste and baby shampoo were laughably ineffective. Finally, I was able to improve the glass by vigorous cleaning and polishing with a liquid rubbing compound made for fiberglass boats. This was a permanent fix. Other stuff like toothpaste and shampoo deposit a hydrophilic film on the mask which is good for an hour or two; after that, the fog starts again. Some divers have reported success through burning the glass with a match or lighter. Upon verification that the mask will not fog, then, thereafter, all that is needed is a spit rinse at the dive site and the mask will not fog for the rest the day. This is because the mask has been "broken in", so to speak.
After you do the mask with toothpaste, remove all residue with alcohol. Wash in fresh water. Spit in the lens. Wash again. Exhale into the lens and watch for fog. If a little fog is formed and disappears immediately the mask is good to go. If patches of fog form and persist, the treatment failed.
About your dealer's comments; it is hard to say if he has direct knowledge of that brand of mask and how to clean it or if he is just repeating something he read on Scubaboard. I will add that there are about 20 threads on SB dealing with this subject.