IATA member airlines and their contractors presumably have real time access to TIMATIC required docs data. Most of us, on the other hand, are limited to free TIMATIC interfaces we find on the internet that might not be completely up to date.
Following is what I see wrt SZX on a free interface:
TWOV (Transit Without Visa):
Passengers with a confirmed onward ticket for a flight to a third country within 24 hours. They can obtain an entry permit on arrival and they must have documents required for the next destination. Passengers with multiple transit stops within China (People's Rep.) must have a total transit time not more than 24 hours.
Exception: This TWOV facility does not apply at Fuzhou (FOC), Huangshan (TXN), Mudanjiang (MDG), Shenzhen (SZX), Urumqi (URC) and Yanji (YNJ).
If the person(s) responsible for ensuring all passengers on your flight meet China's entry requirements sees that you don't have a visa and the above information is what they are going by (once again, I simply don't know if this is the case), it's pretty easy to envision them turning you away. If you were flying inbound to Shenzhen (instead of Beijing) and transiting directly from there to a different country like [MENTION=10152965]ngochaitran[/MENTION], I'd give you higher odds, but I certainly wouldn't recommend this to anyone who isn't already locked into a nonchangable airplane ticket.
As you can see, the list of exception airports is quite short, which means that your Shanghai idea is okay, as long as you make it out within 24 hours of entry.