That is one I wouldn't have thought of. My personal experience -- and the standard disclaimer applies -- is that when I can't reach DNS it is because of a networking issue that would make the server unreachable even if I knew the correct IP address.
Still, thanks, I'll pencil that onto the "thing through when not 3 AM" list.
It's more of a chronic problem than a sitedown problem. You might be surprised how crappy some hosts and resolvers are.
Using dual 3rd-party DNS does give you one very good advantage in acute situations, though. When your host goes down hard you can still repoint domains, receive email, etc.
In general I recommend dispersing services: put your company's blog on a subdomain hosted somewhere else like Weebly, and use something like Google Apps to handle your domain's email routing.
Still, thanks, I'll pencil that onto the "thing through when not 3 AM" list.