Tracy Johnson poses the question:
I'm at a loss to understand how Bryan does it.  Especially a terminal
model that has only a serial port connected directly to a 10baseT port
in the second sentence.

I may have munged up my thoughts on this one.  Basically you leverage
the existing (or in this case newly installed) network wiring by
running your serial terminals over the 10baseT cable.  Most
installations of network wiring will have RJ-45 jacks on the node end
that are connected by individual runs of cat5 cable to some sort of
punch down panel.  Normally you would then run a patch cable from the
punch down panel to a hub, completing the connection.  If you run that
patch cable to a dtc instead you get a serial connection (if you've
plugged a terminal in on the other end).  If your network is more
exotic (ie switched or not on the same side of a router as the dtc)
then this configuration will not work.

I hope this clears the fog from my writing.

Bryan