Apparently, from what I gather, if a 503 is returned the browsers (Chrome/IE10 I've tested) don't parse css, even if they can access them. I've verified this by typing the direct URL to the CSS file hosted on Nginx.
I'm positive my code (HTML/CSS) is right.
So how does one redirect to a page hosted on Nginx acting as a reverse proxy when the backend servers are down, while preserving CSS?