Ahh, i see now where the bus comment came from. I can't speak for Pete, but the way we use RD is not just in case of emergency. we use it to plan the deep stop and deco portion of the dive from beginning to end while we are on the surface and then adjust it underwater if need be.
The way RD was taught to me included a very comprehensive overview of decompression theory from its inception through the various models up to present day. Haldanean, Neo-Haldanean, Bulhlmann, VPM, RGBM, micro-bubble theory, bubble gradient mechanics, oxygen window, exponential curves, s-shaped curves, deep stops, etc were all discussed at great length.
When i compare RD with V-Planner for instance, there are similarities in run-times but differences in the shape of the deco curve. also V-Planner doesn't give deep stops, at least to my knowledge the way i've been using it. i use V-Planner because it's fun to compare schedules. in practice i have only used RD.
the planning is done with paper and pencil (at most) and i use an aladdin tec2g or suunto vyper in gauge mode. i like the tec2 bc it has a nice depth averaging feature.
the beauty of RD is that we dive the same standard gases and the same profiles over and over so you get to monitor how your body reacts to the dives while keeping variables such as gas and schedule to a constant. of course, if something isn't working then you play around with adding time here and subtracting there, etc. it also makes dive planning very easy and quick on the surface for the whole team.
having an idea of how deco *should* work, in an emergency RD will get you out of the water faster and safer (hopefully) if the fit hits the shan. this means knowing where you can shave off time, where it's best not to, etc. i have never had to do this and hopefully i will never have to but that is how it was presented to me.
RD has been used for simple "no-deco" dives and it has been used for dives to 590' and anything in between...
hope this answers your questions.
best,
Ari