The way I understand it, calling a framework RESTful is a bit of a stretch. A framework can be used to build a RESTful application if it allows you to follow the defining constraints of REST. At the same time, it's possible to violate them regardless of the framework. Therefore, no matter how "RESTful" your tools are, you can end up with an application that has nothing to do with REST.
In case of Sling, you can easily create a Servlet, specify that it should use the GET method and have it modify the state of the repository, violating the semantics of the underlying HTTP protocol.
I think what they mean in the Adobe documentation that you referred to is that the default servlets will behave in a way consistent with HTTP, the way Thomas explained in his answer.
However, being consistent with the underlying protocol does not seem enough to call an API RESTful. For instance, I don't really see how Sling (considered in isolation) uses HATEOAS (Hypertext as the Engine of Application State). You need to drive the application state using hypermedia. It makes more sense to me if we consider Sling together with CRXDE, which provides hypermedia controls for resource manipulation.
As for AEM itself, I saw a presentation earlier this year by none other than Roy Fielding himself about REST in AEM and the point he makes is that AEM is RESTful in the sense that it can be used like a website.
- It's navigable
- it uses hypertext (interpreted by the browser) as the engine of application state
- manipulates resources through the exchange of representations
- access methods (as defined by the underlying protocol, HTTP in this case) have the same semantics for all resources.
etc.
It's effectively a website you can use for content management (and more). It can be used by a client (a browser) simply by going to the welcome page and following the hyperlinks, interpreting code retrieved on demand with no need for out-of-band communication (as in reading documentation, building URLs by hand and the like)
Please mind that this answer is my own interpretation of the information I found in AEM and Sling documentation and Roy Fielding's posts and presentations and that it's in no way endorsed or approved by Adobe or Roy Fielding himself ;)