i suspect that you're using their dns server because it's what is given to you via dhcp, but you can probably configure your own (well, you can certainly configure you own; the problem is it's possible that they are blocking dns requests). for example, set things to use 8.8.8.8 as the dns server (which is google's).
comment 5 (in that thread, from the developer involved) says that it is working and testing it myself (google-chrome --dns-server=8.8.8.8) with wireshark shows that it does query that server.
(thanks for pointing this out; it wasn't what i was suggesting - i had assume the laptop was the op's own).
One part of the filter is attached to our default DNS server, and it looks up novel domains to see if they ought to be blocked. This lookup is slow.
Launching Chrome first thing in the morning takes quite a while, because our DNS server/filter blocks until those 3 random domains fail to resolve.
I really wish that I could turn it off, although admittedly our "network" is barely compliant with protocols in the name of filtering.