But, if you summed the market caps of all these companies, what would you get?
My guess is $2-5 billion.
Now Google alone is worth ~$200B.
I agree that you can start a really successful Internet company in NYC. I'd say any city in the U.S. would do. However, if you have some pathological urge to build a gigantic Internet company, you absolutely need to be in Silicon Valley.
Being in the valley is definitely a boon, but calling it a must is silly. Those guys combined have a market cap of $343 billion. The other end of the bullshit-spectrum is people pretending that it doesn't make a difference because they don't want to move.
That said, all startup successes are statistical anomalies. The implicit irrational assumption is that you can beat the odds. Some companies beat harder odds than others, and being outside the valley does set them up for that.
There are lots of reasons one might not want or be able to move -- visas, family, other attachment to a particular place -- and that just has to become part of the calculation, "This makes it x% more likely that I'm just wasting my time, but I'm still [irrationally] convinced I can beat those odds."
We know that this works because there are examples of it. We also know that it's harder because of how relatively few there are.
If all you have is a "me-too"|yet-another-Twitter-client that appeals only to the geek crowd, and has no viable business model, Silicon Valley is the place to be. Especially if you want to burn through early capital living in one of the most expensive locations in North America.
If you want to make a point, you should think of the average company that succeeded, and then see where that company did succeed. For every Google, Intel and Microsoft, there are thousands of startups that did attain success, but did not become giants (not because they failed to become giants, but because few companies are destined to become giants).