While that may be the official party line, in practice it is possible to make such arrangements in a pinch. At least in the consulates with which I deal most frequently, there are plenty of employees who are willing to accomodate if you take the time to ask.

Regarding the initial post, although what christep said is true about US citizens needing a visa to go anywhere in China, there special Shenzhen-only visas available at the land crossing, which are processed on the spot.

Regarding whether to get a visa in the US or HK, if your travel plans include HK and/or you want to get a 6/12 month visa without excessive documention, then HK is the way to go (don't expect to save a whole lot of money though).