Horizontal Dipole - zero degrees elevation

Hello all you antenna experts,
I have been a ham and an engineer for a long time, but I have never
delved into antenna theory. So, consider me a newbie for this
question.

I recently was helping a friend set up a crude antenna to connect to
his DTV converter box following the June 12th conversion to DTV. I
explained that a dipole was a simple antenna that could be used. He
was very interested in the subject so the conversation soon turned to
theory. I explained the 468/freq formula and eventually mentioned
EZNEC. I have never used EZNEC myself so I downloaded the demo
version and now have all of 24 hours experience with it. I started
with the included backyard 20 meter dipole. I was surprised that
there was no radiation toward the horizon. I figured that I was too
close to the ground so I changed the frequency to 491 MHz (RF TV
channel 17) and shortened the dipole accordingly. Still no zero
degree radiation. I raised the dipole to 100' - then 1000' - then
10000' - still no radiation at zero degree elevation. I then found
this in the help section:

-----------------------
Because the far field sky wave from a horizontally polarized source is
zero at a zero elevation angle for any ground type, and a vertically
polarized source produces zero sky wave for any finite-conductivity
ground, attempts to calculate a 2D pattern without the ground wave
component under these conditions will result in an error message.
-----------------------

Sure enough, changing to free space instead of a real ground changed
the pattern to what I would have expected. I would have thought being
many wavelengths above ground would be just as good as free space, but
EZNEC doesn't think so. Am I missing something? Does a horizontal
dipole really have a problem seeing a broadcast TV transmitter out on
the horizon? Thanks. ...Pat
.

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