Can I get a 72 hour waiver if my follow on country does not require a visa?

I am US Citizen living in Singapore. I will fly from Singapore to Beijing (to see Great Wall) and from Beijing to Chiang Mai, Thailand. I think I qualify for the 72 hour waiver while in China, but I am not sure since Thailand does not require one for US Citizens, so I won't be able to show one in my passport when arriving to Beijing. I will have proof of purchase of my follow on airline tickets to Chiang Mai though. Does it sound okay?