I think Google must have a sense of irony as they attempt virtual world domination. Google search, mail, video, browser, chat, voice, maps, docs....and an operating system...to name but a few.
There's a lot to be said about focusing but more importantly having some vision on which to focus. Not being distracted by all the options and alternatives that will almost definitely come your way, but aligning yourself and your business to those ends. In that respect, what you do will remain narrow.
On the other hand growth is about expansion which brings me back to Google, yes they do search facilities well, but that is expanding into many peripheral activities and interests for them. I think their 'one thing', at a high level is 'everything internet'... oh and a bit more.