As a general rule, no that's not true at all. Not until you get to something like 0.1 micron lapping film or Linde B compound or something like that. Maybe then it might be true, but for something like an Escher or Jnat, or 0.5 micron spray media, absolutely not. You won't be able to get away w/ excessive pressure as easily, but you shouldn't be doing that anyway, so it's really a moot point.
Another thing is some stones require a much lighter touch during the finishing stages to yield their full potential for smoothness--they require more skill to use properly is all.
Personally now, I have much less alcohol burn (zero, in fact :)) and a longer lasting shave after shaving w/ a Jnat or Thuringian or even a pasted edge than I do off a coticule edge. Nothing wrong @ all w/ a coticule, but I've personally found I get better (closer, more comfortable) shaves off of other media, and I have slightly sensitive skin, so I don't necessarily buy the "coticule is the best edge for sensitive skin" argument. It sounds just a shade too dogmatic for me...
The best thing to do is try many different finishes honed by people who really know how to get the best of of those hones to figure out what suits you best. It might well be a coticule or it might not. You just have to experiment.