It's really not true. I'd say that it's more Silicon Valley recruiting all over America, than the rest of the US trying to recruit in Silicon Valley. And even if they did, they don't need to pay SV salaries to compete. Salaries adjusted for taxes and living costs is what matters, and other perks such as the City, family friendly areas etc matter too.

And worldwide, Silicon Valley is probably less than 1 percent of all tech hires and less than 10 percent of the top hires. Silicon Valley takes an impressive amount of the top talents for its size, but not most, and almost certainly a decreasing amount. The world is large, and by far the most talents couldn't even get a visa for the US if Google or Apple wanted them.