In fact these do exist. I saw a demo a few years back from a company that tracked bogus GPS signals and how they could watch jammers drive around the streets of London all day long.
These guys were doing it because they were tasked with keeping LTE towers synchronized and they did it with GPS time so they were building in resilience to their time sources by measuring the signal level and rejecting anything that came in too strong. Spotting jammers was a side benefit.
The GPS antenna on the LTE tower should only be picking up signals from the sky. Transmitters on trucks would need to reflect off of aircraft in order to cause trouble, which would greatly weaken the signal.
Yes the antenna pattern will attenuate the signal coming from the ground somewhat, but it also doesn't suffer from 182 dB of freespace attenuation like the real signal. It doesn't have to bounce off of an airplane either, the Earth has a layer of atmosphere around it that gets ionized by the sun and is also full of water vapor. We also don't have the ability to build perfect antennas, especially since it has to cover the entire sky (GPS antennas do not physically track the individual satellites).
