As far as I can see this has nothing to do with the Internet tablet (or even your desktop computer). You get handled a DNS address from your DHCP server, and if not, then you're told which DNS to use, and what's to use and which root DNS servers to be used is a question for the system admin on the site which either hands out DHCP configs or manual configs.

p.s. There's a lot of rubbish in that newsforge article, for example:
"After switching to OpenDNS, [...] ping times were considerably lower,"...
ping times have nothing to do with DNS, it's purely a question of the physical network structure (and load) between you and where you ping. DNS is only involved in the translation from name to IP, which happens right at the beginning and how long that takes isn't particulately interesting - that's not why you're pinging.