"Once a directory stream is closed, all further method invocations on the iterator throw ConcurrentModificationException with cause ClosedDirectoryStreamException".

At this time (jdk7-b71), the remove method does not wrap the ClosedDirectoryStreamException in a CME.
A second issue is that next/hasNext throw ConcurrentModificationException(IllegalStateException) rather than the more specific ConcurrentModificationException(ClosedDirectoryStreamException) as specified.