US citizens can certainly get a regular Chinese tourist visa before they leave from the Chinese embassy or consulate in the US that covers their state of residence. A single-entry visa that would be valid for travel all over China for up to 30 days certainly could be used for a day trip of a few hours into Shenzhen from Hong Kong. So it's not true to say "US citizens can't get a visa to go to Shenzhen."

Two other questions are: a) can you get a Shenzhen-only visa issued at the border like you used to be able to do with a US passport, and b) can you get a Shenzhen-only or regular Chinese visa issued in Hong Kong with a US passport.

I think the answer to both is "no" but hopefully someone with specific knowledge can chime in.