Yes there are lots of kids in SF trying to get their website turned into the next unicorn. That does not make SF the "center of the tech world", it makes it the "center of the SF tech startup world".
The density of tech startups in SF is much lower, more like New York. Most of them are just retail companies (shops) or food services. Yes, Pinterest, uber, lift, twitter have serious tech problems to solve involving scale, but companies like that are in the minority. And businesses where people develop new technologies are more common in the Valley.
Living in the city and commuting to the Valley was already the norm when I got here in the early 80s.
The point isn't to have a pissing match. I'm simply pointing out that the heavyweight tech region is the San Francisco Bay area but within it the tech influence is unevenly distributed which should hardly be remarkable.
It's easier to find marketing, PR, non-B2B sales folks, web designers, ruby developers etc in SF than down here. It's way easier to find people down here who understand interrupt latency on 32-bit arm cores, oddities of device physics below .14 nm, B2B BD folks and the like. Does one diminish the other? No.
Reporters from outside of course go to SF to report because, frankly, what's to see in Palo Alto? I have lived in Palo Alto for decades and yes, apart from the work (which is awesome) it's dull compared to SF, or even to many places lamer than SF.
I moved to Mountain View to found a startup a few months ago. When I think about the "chat over coffee" type of meetings go, I would say that there may be slightly more of them in San Francisco than South Bay.
It feels like San Francisco starts to outweigh Silicon Valley. I didn't do precise calculation, but estimation based on my gut feelings would say that ratio of "Seed stage" startups between SF and South bay is 2/1.