It makes sense, if you can't write to it then you can't damn well install it. If only the installation would take care of those issues automatically, eh?
Make sure to issue chmod 777 (that's read and writer permissions) for the ff: folders:
In fact the JoomlaHack Tip #3 mentions having to change file and folder permissions. Earlier in 2007 and later in 2008 there are several posts from QNAPAndy that mention this needs to be done for everything under the /share/Qweb subfolder.
I have recommended about the same for WordPress in this QNAP Forum thread.