REST is an architectural pattern that specifies properties about the interface, not the data - how does using JSON over XML make your interface not RESTful? In his dissertation[1], Roy Fielding always refers to data in terms of resources rather than specific formats.
I think the idea that JSON isn't "REST" is because, unlike XML, it doesn't define links.
That said, JSON is just an encoding format. The actual response format is not "JSON", but the specific structure that your clients are expecting to receive (even if it is encoded in JSON), and that can certainly have links.
That said, JSON is just an encoding format. The actual response format is not "JSON", but the specific structure that your clients are expecting to receive (even if it is encoded in JSON), and that can certainly have links.