I'm from Chicago and while the startup scene there is pretty solid (cheap rent, large city, big financial center for funding) SF Bay is in a league of its own (maybe NYC also).
That doesn't mean you won't find investors, resources, etc in other cities. Is basically the same as asking whether you should go to a top 10 school or go to a top 50 school. You can have the same amount of success at both opportunities its just how much effort you put into it.
Moving to silicon valley won't make your business successful, but it will give you access to the tools and connections you need to help yourself. These same tools exist elsewhere but you might have to search a bit harder.
The thing with starting a company is its very rarely just you that is involved in the enterprise; you need developers, you need designers, you need bd people. People that do these things for startups tend to have a slightly different slant or skill-set than people that do them for large companies. As a result, it is a distinct advantage to be near large population centers that have a wealth of this talent.
One of the contributing factors to this is the organization that spawned the very website this is posted to; YCombinator based in SV and companies doing a class move to the bay area for it. The gravity is strong here.
Can you start a company outside the valley? Yes. Is it going to make things much more difficult for yourself doing so? Probably.
Another contributing factor to the dispersion of startups that hasn't been mentioned is remote work. It is possible to have an office in SF and keep yourself and your family elsewhere.
I would love to see data on this one way or another. I find it very hard to believe that it is quantifiably more difficult to start a company outside of Silicon Valley. But you are not the first person to state that.
Django (excluding python specific): MV: 2231, NYC: 2120, Austin: 41, Chicago: 126
RoR (excluding ruby only) MV: 4119, NYC: 4390, Austin: 158, Chicago: 417
I could probably go deeper but at least from a glance it is easy to see why starting in NYC or SF would be preferable.
NY, Seattle, Boston, Northern Virginia / DC, Los Angeles - are all excellent start-up destinations depending on your needs.
There are second tier start-up locations as well that can be quite nice, such as the research triangle in North Carolina or Dallas - Fort Worth. If you're in energy, perhaps Houston (it continues to boom); if you're in biotech / pharma, perhaps San Diego. Denver and Portland can be nice for lifestyle purposes. And so on.
SF/Bay Area is truly head and shoulders above anywhere else for startups. Like Shaquille O'neal's head and shoulders.
That said, it doesn't make it impossible elsewhere.