I do it all of those ways and others besides. Juranitch is full of crap and doesn't understand how natural and composite stones work. In order for a hone that is a composite of grit to work it has to constantly wear down and expose fresh grit. Oil stones are intended to break down at an optimal rate if wet with oil and waterstones are intended to break down at an optimal rate if wet with water. For short periods of time you can use these hones dry, but then you need to clean and freshen the surfaces with something like a sink cleanser and some scrubbing. The use of oil probably started because natural stones responded well to using that.
Now oil is messy so I experiment with other fluids to achieve the same effect. The right fluid prevents loose grit from caking in the surface of your hone as well as allowing a gradual hone wear (which exposes fresh sharp grit). On natural Arkansas hones for example I like to use rubbing alcohol.
Ceramic hones resist breaking down with fluids and work pretty well dry. I say "pretty well" since their surfaces do get filled with metal residue. You have to scrub them to remove that metal periodically. You never have to do something like that with an oilstone or a waterstone that has been consistently used with its proper fluid.
Diamond grit hones are made more like sandpaper than like a hone. You don't want those to break down since there would be no grit left once the single layer was gone. They are set in a very tough substrate and diamond is incredibly hard so you don't have wear expose new grit, you just keep using the same grit layer. The diamonds are slippery and metal does not stick to them. With a diamond hone you generally work dry and just wipe residue off periodically with a rag.
I like to work with a clean hone that does not have a bunch of loose grit on the surface (its not usually a big deal, just a minor preference). What I often do is hone under running water. This works with a lot of different types of hones if I have made sure that they don't have a residue of oil embedded in the surface. I have used aluminum oxide, silicon carbide, waterstones, diamond hones and even ceramic hones that way. It insures that no grit residue dings or rounds my edge.