Its not a file in this case. It is RESTful URL, .json part just asks server to return results in JSON format. Probably you can use /model/user.xml to get response in XML format. Twitter and many other services does this the same way.
Another common way to request specific response format is by providing HTTP Accept header.
For further reading I recommend this resource: http://blog.2partsmagic.com/restful-uri-design
Some applications return different data if the user adds a different extension. e.g. they may ask for contacts.xml or contacts.json. But different URIs imply different resources. Are the two data formats really two different resources? Or just two different representations of the same resource.