Besides assets, rich text area images are also visible on a Site.com site, though they are within the context of a value of a rich text area field's data for a row via a repeater.

To make documents and Visualforce static resources visible, it's presently required to use Force.com Sites. The Site.com site can reference the documents and Visualforce static resources by URL, though constructing those URLs isn't as seamless as it is in Visualforce, and some trial-and-error might be needed to construct the proper URL that Force.com Sites expects to access a specific document by its Id or a Visualforce static resource by its name.

If using Visualforce static resources from a Site.com site, it's important to note that the version number part of the path in the URL in a static resource isn't required, but it helps greatly with ensuring that the latest version is always served up while allowing systems to cache them for a long time. You will need to change this version number manually in the URL whenever the static resource gets updated to ensure that web browsers won't use the older version. For now, it's generally recommended to not reference on a Site.com site any Visualforce static resources that live on a Force.com Site.

For now, using Site.com assets is the preferred and supported approach.