I think that is a permission problem as well. One solution might be to add the user you are normally logged in with to the "public" group.
To find out exactly which user you are logged in with (from a terminal: K > System > Konsole):
For the DVD installer this will likely be linuxmce, for the CD install it will probably be the user you created during the kubuntu install.
Then edit /etc/group (you can use any editor besides "kate" if you like):
sudo kate /etc/group
And change this line:
To include the username you found earlier in the previous step, for example linuxmce:
Now you should be allowed to copy files to the directories under /home/public/data/.