Again...this isn't "Beijing getting its way". This is "Beijing trying to figure out a way to handle the clusterfuck that Shandong created without looking like they have no handle on the situation whatsoever". Corrupt local and provincial governments have been the bane of China's existence since time immemorial. And at least half the time, the central authority -- be it the Emperor or the CCP -- are in the role of the benevolent power that can protect the peasants from the corrupt local officials. The other half of the time, you had terrible Emperors who were just as bad or worse than the local magistrates, and you had to hope you lived under the occasional good magistrate or governor who ignored the Emperor's demands.
China is the world's largest bureaucracy. Which means that no matter how reform-minded the central government might be, it faces major opposition from its subordinates who have an interest in maintaining the status quo and are already entrenched and have plenty of layers of red tape to shield themselves. Once the Shandong authorities have arrested Chen, Beijing can't just step in and tell them to let him go. Not without their own investigation and good evidence to show that the Shandong authorities were corrupt and that Chen is innocent. Now, to their credit, Beijing has said that they want to launch their own investigation. Hopefully, they'll actually figure out who was responsible and smack them down.
Of course, from the outside, most people will see "internal investigation" and assume it's a cover-up or that nothing will result from it. That's not necessarily the case. When local officials are corrupt but it doesn't make the news, shit does tend to go unpunished. When it makes the news and people are talking about it, shit gets done. When officials were taking bribes to look the other way and let contaminated milk into the supply? Probably would have been ignored until kids start dying and people started getting pissed off. And most of all, Chinese milk products started getting banned for export. Next thing you know, those officials are up against a wall with a blindfold and a firing squad. The corollary to that is that when local officials are corrupt, and their victims begin making noise and bringing attention to it, they (the local officials) crack down even harder, because they know if Beijing finds out the full details, they'll be kicked out of their cushy post at best, and facing a firing squad at worst.
My guess is that while Beijing and the US were working out this agreement to transfer Chen to somewhere else, somebody from the Shandong government passed a threat to him reminding him that his extended family still lives there, and if he knows what's good for them, he'll shut up and not tell Beijing anything else regarding their corruption. Hence, his very reasonable decision to pack up the family and get the hell out of Zhongguo, out of reach of the Shandong authorities.
That's a win for Chen (sort of...being forced into asylum in a foreign country probably isn't high on his list of life goals), and it's a win for the Shandong officials, because he's out of sight, out of mind, and they'll likely get off without a penalty. It's a loss for Beijing, because they look powerless to punish corruption in their territory, powerless to prevent their citizenry from fleeing the country, and powerless to keep the US out of its domestic affairs. It's also a loss for the US because it makes it look like we're trying to intervene, and it opens up the door for more and more dissidents to try and use the US as an escape plan when things get too hot. Honestly, Beijing needs these sort of people to remain in China and help them root out corruption at the local levels. They know it's there, they probably even know which officials are the worst, but without hard evidence and some weight of popular opinion on their side, it's incredibly difficult for them to penetrate the web of favors and kickbacks and entrenched interests and actually remove the worst offenders.
I know that sounds completely insane, but that's how it is (and I should note that decentralization of power and the struggles of the center against the provinces, in both China and India, was the subject of my master's thesis...I'm not just talking out my ass here).