IMHO, Shortening/butter only affects royal because of how/what you are making. Royal is basically a meringue as it's sugar and eggs whipped for ten flippin minutes (i would never have the patience, how do you all do it??) Adding grease to a meringue breaks down the whites and they cannot hold all the air bubbles that you are trying to whip into them.
On the other hand, if you start with a shortening/butter based icing and add some meringue powder you get a crusting buttercream. There are a lot of threads on here about crusting buttercream and whether the meringue powder actually does anything. The general consensus seems to be.. maybe.
The basic idea is that it helps it firm up a bit faster and stabilizes it so it can stand up to high humidity/heat conditions. I don't think it works as well for the cakers because they use much thicker layers of icing. I've used it once and as long as i left it for 24hrs it firmed up completely and was still soft and edible. (i have a pic)
Basically, the oil/egg white rule depends on what you are trying to do with your whites. If you want them whipped stiff and full of air then yes stay far away from oil. If you just want to boost stability and drying time in another icing then, IMO, you're fine.
Judging from the ingredients list someone posted earlier and from the pics on their website, I would hazard a guess that they use some sort of shortening based crusting buttercream. You can see the piped lines in the small filled in areas because the consistency is so much thicker than other icings. To get the background smooth they probably trowel the stuff on then scrape the top smooth. Actually, other areas look so smooth that they may have used a rbc, but it's hard to tell. If you look at the "chicks in disguise" basket they have up now, some of the details on the eggs are definitely not piped.
Sorry this is so long. I'm kind of bored right now...