Hi, we don't understand why if someone share a document with you, for example, you see it in Drive, but if they share a Site with you, you don't see it as a Reader of published versions, only if you're an editor.
I think Google doesn't really treat Sites as "documents", hence, they don't show up in Drive like other document types (unless you're the editor). Viewers of the site are supposed to look at it as what it is: A website.