8-12 August in Beijing and Hebei region

Hello
I'm Italian and I'm planning a tour in China this summer.
I will land in Capital International Airport on 8 August in the early morning (Finnair flight with stop in Helsinki) and I will leave the city from the same airport on 12 August in the evening (honk Kong Airlines flight - no stops).
I will stay in the city and would like to visit also the great wall, the Ming Tombs and Summer Palace.
Am I eligible for the visa exemption?
In particular: I heard that it is possible to apply for the 144-hour visa exemption only taking the same airline company for both the inbound and outbound flights. Is it true?

Thanks!