Well, this is puzzleing, as I just did a new "one-click" install of my own to duplicate your problem, and had no problems.
In all of my joomla installs (ver 1.0 - ver 1.03), including the last "test" one that I just completed, the session_save directory is set as "/tmp", which is a directory immediatly off the root of your server. It is owned by DH, and is, by default, writable by all users. You should not have to add any directory for that, and Joomla has always used that directory sucessfully for me.
We are gonna have to dig into this a little more:
1) Since you used the one-click install, did you notice the directory was unwriteable at install time (when following the links provided in the "success" email sent from DH) or are you responding to an error message?
2) what server are you on?
Question 2 is important, because it is about the only "difference" between our installs - both were done with the "opne-click" installer on DH. I suppose it is possible that your server is mis-configured in some way, though that seems unlikely as any DH server with an unwritable "tmp" directory would probably have caused all kinds of support requests by now.
3) can you include the url of your "broken" installation, so I can visit and have a look?
Don't get discouraged; Joomla works great on DH, and we will get this figured out.