Can I apply for 144-hour visa free transit with combination of air tickets?

Hello,
I have bought two separate air tickets: Hong Kong - Tianjin and then Beijing - Prague. According to your article I am eligible to apply for the 144 hour visa-free transit, but when I asked the Czech embassy in BJ via email, they replied to me that I cannot apply for 144-hour visa free transit when it is not just one air ticket (e.g. HK - BJ - Prague or HK - Tianjin - Prague). Is it true? Does anyone have any experience with that? Because I think that maybe they are wrong. According to the 144-hour visa free transit policy you can freely move within the area BJ - Tianjin - Hebei, so why should they care whether you travel to the country C within one air ticket or whether you bought another one..?
Thank you very much for any reply.