It's not as dumb as you guys might think.
Basically, the policeman in charge just hides away those plates which have nice number combination like 518, 666, 888 etc and he will give the priority of choosing the number to his friends who know the meaning of "gratitude"! The policemen are very well paid in China comparing to other wage receivers, a rookie police officer got around 100,000 RMB/Year (10,000 EURO) in Xiaoshan (Hangzhou), Zhejiang these days. They don't need a helluva cash, they just want their life to be more comfortable, distributiing favorable numbers to a certain group of people will certainly benefit their future career. That's all about it, no such dumb person would actually ask for money and risk their professional life.
You need around 40,000 RMB to buy a Shanghai plate, that's why quite a lot Shanghainese are regestrering their cars in other regions like Zhejiang and Jiangsu province where the expense is much less expensive, but with a provincial plate in Shanghai sometimes brings about a lot inconvenience. Don't know about the situation in Beijing tho.