Rails is not using my global Ruby version
You didn't tell how you installed rbenv, but I think it is per-user installation (which is default). In this case you should install gems without using sudo. When you did sudo gem install rails, it was installed in system ruby, not rbenv's selected one.
Solution - install rails without sudo:
rbenv global 2.1.0gem install railsrbenv rehash
Sounds silly, but did you restart terminal session?
Otherwise try and type
/bin/bash --login
Try creating a .ruby-version file in the root of your project with the following contents:
2.1.0