I think, what you mean by structure of JSON is the structure of individual documents encoded in JSON, not JSON format itself. In the case of JSON format itself no agreement is necessary. As long as both programs implement the format definition, they are good to go and don't need to be aware of the existence of the other. This is evidenced by, eg. ability of text editors to edit JSON files w/o needing any knowledge about the producer of the file.

Compare this to, for example, Protobuf, where once you get the binary Protobuf message, you absolutely have to know what program generated it and how, otherwise you will not be able to read it. You cannot make a generic Protobuf editor the same way you can make a generic JSON editor.