It is not really possible for outsiders to tell how orders are being moved around within the party mechanism. China's message is that the regional government is at fault, but that's what they always say when there is an expression of discontent among their people. It is not "kosher" for the central government to take the blame for anything, so you can never really believe it when someone else takes the blame. Maybe the CIA knows, but anyone who isn't tapping internal communications is not likely to get beyond speculation.
In any case, a culture of honesty has to start at the top, and it is likely that the local government "knew what not to report." There are many situations where the claim that no official report was given to the central government would be true, while at the same time the central government played a role in the suppression. So as for speculation, I would say that there are many possibilities where the central government had a role to play in the suppression (even if it was played over years before), but only one possibility where the local authority went off and did something totally out of line.
Edit:
>The laboratory findings were relayed to officials in Beijing at the Centre for Disease Control (CDC). The information should have alerted national health chiefs to a looming crisis, but on January 3, the National Health Commission, China’s top medical authority, issued its own gagging orders. Laboratories were told not to release any information and to hand over or destroy the samples.
Well, it looks like the local government didn't know what not to report after all. (Thanks to makomk's comment for pointing this out.)