Sounds believable that countries do these alerts for sometimes political reasons, but China is actually keeping people from leaving the country for unspecified reasons and is seizing people, even their own citizens.
The reason why those seizures are happening is why this "escalatory" bulletin is newsworthy.
This is another bullet point in an escalation trend we've been seeing between the West and China, mostly surrounding infrastructure and political pressure/flurries of arrests and high profile detainments, in both regions.
China's warning is related with US randomly violence, gun shooting, robbery etc (if you understand Chinese: http://www.china-embassy.org/chn/lszj/zytz/t1597786.htm). US and China are very different countries, like in China, the downtown of metropolis is very safe at night, but in US is totally different. And also, gun shooting in US is really normal, but extremely rare in China.
This reads like an faq for people coming to US. First item reminds people to buy travel/health insurance. Second item warns against going out alone in late night. Etc. I didn't see anything political in it.
I'm not saying it's OK, but it's hardly a reason to warn people not to go there.