I've used both over the years. To me they are similar (although not identical) products. I seem to recall they both smelled like banana flavored candy to me for example. But Chemiclean is a white powder and RSM is a yellow powder. They might not be the same thing. I think you can also use Erithromycin but I've never tried this myself so don't quote me on that.
I think in a way they are both right because the same sort of thing happens with either of them: 1) the skimmer goes nuts, and 2) the O2 level depletes in the tank as the cyano starts to die off and rot, thereby increasing the risk of suffocation/asphyxiation of the tankmates.
Therefore, leaving the skimmer "on" means it will likely overflow and make a mess, and leaving it "off" takes away something that helps with re-oxygenation. Nothing is black or white, but there are a million shades of grey.
My advice is:
1) If the skimmer is in the sump, just leave it on and let it overflow back into the tank, as there is no risk of flooding your floor or emptying your sump.
2) If the skimmer is a hang on the back style, or external to the sump, then leave it on, but dial the air intake as far down as possible. Lower the water level in the skimmer if you can too. This way it's still bubbling away, but not emptying the tank.
3) If you don't have a skimmer at all then stop being so eccentric and just go out and buy one. (JUST KIDDING. Sheesh, put the tomatoes away. Everyone's a critic..
). But seriously, if no skimmer, then maybe add a powerhead to agitate the water surface or something like that just to keep up with the O2/CO2 exchange.
Hope this helps..