You should not copy files from the var/run/classes/ directory to classes/ - they just won't work as the class inheritance tree is different there. What the documentation say is that once you created a module and re-deployed the site (so its classes have been compiled into var/run/classes/), you can tweak the compiled files in the var/run/classes/ directory, debug the site without re-deploying it and, when you have a working code, transfer the changes (not changed files!) back to the classes/ directory.
Moreover, in the new 5.3.x version the process is now smoother: when you enable the developer mode XC5 will track changes in the classes/ directory and will re-compile changed files automatically. So, now you don't have to hassle with transferring changes between var/run/classes <-> classes/ directories. The same happens with template files when you are in the developer mode - you can tweak templates in the skins/ directory and XC5 will compile them into the var/ directory automatically.
Please check this article:
http://devs.x-cart.com/en/what_is_new/what_is_new_in_5_3.html