There's two ways to assign authorization. The controller class or the ActionResult. As opposed to how else you could do it, I'm not very sure.
I don't really see the side of the argument where you argue against the controller managing who's authorized to invoke it. By having the authorization nearby, you follow theory (I forget the name) of 'declare it as close as you can to where you use it.'
It might depend on the background of your coworkers. If they're really used to using something like XML, then I bet they're suggesting some type of configuration file - which seems to be induced due to a more corporate type of programming.
On the flip side, There could be a benefit to extracting out authorization somewhere else (but within the application) so that it's easily modifiable, in case you end up adding a "PaidUser" for example. In that case you wouldn't have to go to every controller to update it. However, I think you end up falling into an all or nothing approach - where it's either in the controller, or it's all in some configuration file. Unless you create a scheme that your central authorization can be overridden by a controller's authorization, except at that point, you can easily lose control of who's managing what and you end up in an 'authorization soup' of sorts.