Had a quick look at my own car policy - it specifically excludes (amongst other things):
Any accident, injury, loss or damage when your car is in an area where aircraft are usually to be found taking off, landing, manoeuvring or parked or in an area where airport ground equipment is parked or on service roads leading to it.
This appears to allow driving past the gate as long as areas containing aircraft are avoided. I suppose to be rigourous the definition of "area" would itself need to be specified...
On another note, I have £10m public liability cover whilst scuba diving covered via my BSAC membership (£65.50/yr). Apples and oranges (I would struggle to damage a Citation with a snorkel), but simply using this as an example that it should not be overly expensive to get sufficient cover.