This flies in the face of the so-called "freeze-for-freeze" process China has long championed, which would have seen North Korea halt its weapons tests with the US and South Korea simultaneously stopping their joint military exercises.
It is also very far from China's ideal nuke-free, US military-free Korean Peninsula, and Dr Graham said this may have been part of the point.
"Kim Jong-un wants to make it clear that he is making the running here on his own terms," he said.
"One obvious way to do that is to separate his position from that of Beijing on the freeze-for-freeze formula."
Dr Graham said North Korea has form in this area: Mr Kim's father, Kim Jong-il, reportedly made similar comments at an earlier inter-Korean summit in 2000.
According to his South Korean counterpart, Kim Jong-il said US troops must remain for the sake of "stability and peace in East Asia."
"The obvious logic arising from that is that North Korea also seeks some sort of balance against China. That's what I think the Chinese are most frustrated about," Dr Graham said.
North will want 'strategic independence' from China
Photo: North Korea and China have been close since the days of Kim Il-sung and Mao Zedong. (Getty Images: VCG)
While North Korea's alliance with China protects it against foreign military intervention, Dr Graham said the North has never been shy about maintaining "strategic independence" from China.