If the entire JSON-structure had to be rewritten to disk after each change to keep it persisted, it wouldn't be a very good database.
I would say this is not true of any document database I know of. For example, Mongo doesn't store documents as JSON, it stores them as BSON (http://en.wikipedia.org/wiki/BSON).
Also databases like Mongo will store documents in RAM and persist them to disk later.
In fact many document databases will follow that pattern of storing documents in main memory and then writing them to disk.
But the fact that a given document database will write data to disk - and the fact that some documents might get changed a lot - does not mean the database is non-performant. I wouldn't disregard document databases based on speculation.