staying in shanghai for 1 night - need a visa?


I'm flying from Singapore to Shanghai via Hong Kong on June 20th, and I am flying to the US on a separate ticket the next day (I am a US citizen).  I have read many websites that say I will not need a visa for this (including the Chinese Embassy in the US and the US State Department), but I was just curious if anyone has actually tried this (staying in Shanghai city for less than 48 hours, with tickets and a visa for onward destination).  Does it actually work, or should I go ahead and get a transit visa anyway (I would think the airline might not like it if I try to fly to China with no visa)? 

Any advice would be greatly appreciated.

Also, just to be clear about the last part of my post, I am flying one airline into Shanghai and a different one out, so I will not be checked all the way through to my final destination in Singapore (i.e., how do I convince my first airline that I do not need a visa?).

The thing is that often Chinese authorities seem to be reluctant to publicize policies that benefit foreigners. They'd rather emphasize the general rule that foreign visitors need visa to enter China. The visa-free transit policy applies to cities of certain countries, including Japan, Singapore, South Korea, the U.S., Canada, Australia, New Zealand, and most of the European countries. Applicable to Pudong and Hongqiao Airpor. In situations where there are uncertainties, such as flying on different airlines, one might as well get a visa, just so to have the peace of mind,.