Can't add rewrite rule for static files with add_rewrite_rule function

I’m using the WordPress add_rewrite_rule function to intercept requests to CSS and JS files, and this works fine in a local Apache environment, but the rewrite rules don’t seem to fire in the WPMU DEV Nginx environment. I simply receive a 404 response.

Is this a shortcoming of WPMU DEV’s hosting, or is there a way to work around it?