I think you have identified good incentives, though I believe that in practice what we have seen is local officials being punished for hiding the facts from the top part of the gov't more than anything (the narrative could go both ways).
But I think you are confusing China for North Korea a bit here. Loads of people (including people who have basically zero interactions with foreigners) have VPNs, and access to outside information (if only just to have access to certain websites including just for work or cuz they want to look at Youtube). I'm not talking about activist types, just people who want to use the internet without too many issues.
And locals do post about what is going on, protests and the like, for various things all the time! Now it's stuff that gets deleted pretty quickly in many cases, but it's how information travels! And people save videos, it gets passed around on the open web...
There are also, of course, all the Chinese natives living outside of China, who all have contact with relatives and can be discussing things constantly. Of course people within the country might have a skewed vision, but at one point you would have enough people connecting the dots to have a real story.
China is not sitting around listening to every video call happening between relatives, holding the finger over the "cut communications" button like they are with CNN! I would not be surprised at them applying a lot of evil stuff at all outbound communications for their reasons, but it's not 1984-style magic!
I don't want to be too definitive about this because everything can be surprising, but at the end of the day if a bunch of people around you are dying that will affect you in a material way and I doubt you would keep it secret.
I wouldn't be surprised about a bunch of people having minor cases, and maybe hospitalizations can be kept more under wrap if there is a recovery there. But the idea that "we lock down entire areas when we find cases" works feels almost like a null hypothesis to me.