Upgrading from 4.x to 5.x you can use the first link. Changing the rhoconnect version in RC's gemfile and bundle install is sufficient
Thanks, Krishna, that confirms my suspicions!
The documentation is pretty significantly out of sync with reality.
My experience was pretty-much as you describe. I poked around and found that our project was for the most part already set-up as shown for 5.x. So, I think the documentation incorrectly gives instructions for updating from <4.0 as instructions for updating from 4.x. I say "for the most part", because of course the project had changes from it's initial generation, and of course had accumulated it's own unique additions.
I did find one little secret, which is that you also need to update .rcgemfile, not mentioned in the docs. I created a fresh RhoConnect example from 5.1.1 commandline, and updated from the .rcgemfile that it created.
After that, I was able to successfully update the project to 5.1.1.