I partially agree. You can't pitch a web hosting company this way, because they're commodities, and every web hosting company is essentially the same.
Luckily, investors like Richard Branson want ideas to be _new_ in order to be worthy of investment. And if you want to do something new, then you should be able to explain what's new in a few words. 111 characters is an arbitrary limit, but it's not terrible.
Amazon is new because it cuts out the middle man, and promises better margins for publisher and customer alike. That sounds like a good idea right away. Also, not everybody lives close to a Barnes & Noble, so the idea of delivery of books is by itself cool.
With an elevator pitch you only have a few seconds anyway. So you simply HAVE to convey as much as possible in as little time as possible. When you restrict yourself to a number of characters you can try to fit as much as possible in there. A much better metric than "3 sentences" or "10 seconds", because those two metrics can be gamed (sub sentences and talking rapidly).
111 characters is a gimmick, sure. But it's a _cool_ gimmick.