You are correct, the data is not stored in the database but in the filesystem itself, it is also important to note that the file is not "read in" to the database when it is placed on the filesystem, implying that it is copied to another location, it is actually stored as an NTFS file and the FileStream APIs show the file metadata inside the filetable.
The filetable is built on FileStream technology that was introduced in SQL 2008 but allows you to directly modify the data via windows explorer.
When you create your database, you specify that one of the filegroups is a filestream filegroup, this isn't like a normal filegroup and is actually a series of NTFS folders called Data Containers, this is where your files actually get stored, you can't modify this folder directly, but you can look at the contents (not that there's much human readable stuff in here though, you can find your actual files in here though if you look hard enough through the GUID folders and oddly named files :)).
The file share that you use to copy the files into the table is actually a representation of the data inside these data containers that is presented to Windows explorer via a filter driver which uses the streaming APIs to make the changes to the data containers and add the rows to the filetable etc.