Consider the actual resistance (or more precisely, the impedance) of soil... It is often hundreds or even thousands of ohms when measured at a single isolated ground rod. If you have a fault that puts a live conductor in contact with your isolated ground rod it's rare that enough current would flow to trip a breaker or blow a fuse. In that scenario, you could have 120 volts standing on the antenna system, including the exposed cable connectors and even the TV chassis.
"So what's the point of a ground rod?", one might ask... In the case of your home's electrical service, the ground rod or other equivalent connection to earth serves one purpose, to provide a path to earth for static or induced charges... preventing the build-up of a large static potential between the home wiring system and earth.
Based on your description, your antenna system is probably protected from static build-up but it's not protected from the hazard that would occur if a 120VAC line came in contact with any part of the antenna system. It's unlikely that a single ground rod will provide a sufficiently low impedance to trip a breaker or blow a fuse.
The solution is called 'bonding'. The term 'grounding' is often used as though it is synonymous with 'bonding'... The two terms are often related and/or complementary, but not the same.
The NEC calls for a bonding connection between the mast and the electrical service grounding system... using a #10 AWG copper conductor (there are a few alternatives listed). The NEC also calls for bonding connection between the coax shield and the electrical service grounding system. The use of a heavy gauge conductor avoids the problem high resistance soil, so you can count on the #10 copper to conduct enough current to trip a breaker or blow a fuse if a nail gets drive through a coax and adjacent Romex cable.
An option some may use would be to bond the antenna ground rod to the electrical service grounding conductor. The NEC says that should be done with a #6 AWG copper conductor which is more expensive than #10 AWG, so I don't see it done very often.
For what it's worth, the soil here in the Puget Sound Region is often sandy glacial till and I have on several occasions, connected a light bulb to a newly driven ground rod and applied 120 VAC... I have yet to see a 40 watt bulb light up. While doing this experiment, I've measured the current through the bulb using a known accurate AC ammeter... based on the measured current, a 5/8"x8' copper clad rod has about 1500 ohms impedance. Even with the bulb removed and the 120 volt line connected directly to the rod, the current was only about 80 milliamps. During this experiment, the voltage between the hot and neutral (which was not connected to anything) of the power cord remained constant at around 120 volts.
Ground rods don't provide bonding.
I have run mast bonding quite some distances when the antenna system was distant from the electrical service. In some cases, I've driven a rod near the mast, but I ran a #6 AWG bond back to the electrical service as called for in the NEC. The reason I chose to do that was because the coax run went into underground conduit between the mast and house... I wanted to bond the coax just before it went underground, otherwise it would have been more economical to run #10 AWG to the mast and run the coax past the electrical service and bond it prior to entering the house.
Have a look at this thread...
http://forum.tvfool.com/showthread.php?t=901 Particularly post #20