I’ve tracked down the problem: the rails_multisite gem has restrictive permissions on some of the files, and so the vagrant user can’t read them (and hence can’t load the code).
While @sam is unavailable to make a new (fixed) release of rails_multisite, the simplest workaround is to run the following:
sudo chmod -R a+r /var/lib/gems/2.2.0/gems/rails_multisite-1.0.2
That’ll fix the permissions and you’ll be off and running.