From my limited testing (done some more since previous post) it seems that a database
can be taken offline and brought online even if a snapshot exists and
changes have been made since the snapshot was taken. This makes sense if you think about it because snapshots are used for restore purposes and so if you are happy to persist your changes (i.e. you don't want to restore), there should be no reason why you can't then take a database offline and bring it back online again.
However, if a file is taken offline (using ALTER DATABASE MODIFY FILE (NAME = , OFFLINE)), it can only be brought online by restoring the file from a backup...and that's what the existence of a snapshot prevents.
As I said previously, it is not possible to take a FILEGROUP offline explicitly, but because taking a FILE offline makes all the objects in the filegroup that the file belongs to inaccessible, it is essentially the same thing.
So to go back to the original post, I think that answer is correct but the question should have referred to a FILE rather than a FILEGROUP.
On a sidenote, an interesting behaviour of taking a database offline using Management Studio (as opposed to T-SQL) is that if you cancel the offline command, say because you realise you have an open connection to the database, the database will still go offline once the open connection has been closed, i.e. cancelling has no effect.