Clarification of 72 hour visa free transit

Can you please make a clearer definition on your site regarding the 72 hour free transit.

We were refused to enter the plane from Stockholm to Shanghai via Beijing. We didn't understand that we were not allowed to change planes in Beijing to use the free transit in Shanghai. We think you need a precise description of this to avoid future misunderstandings.

We were several people reading your descriptions and we didn't understand the limitation until afterwards. We have lost a lot of money and time.