Dave, I think the problem is that you are mixing up ideal components and real ones.

The planet is no more a real electrical earth than a wire is a perfect conductor. Real wires have resistance.
Real earths can be disturbed by electrical input. Since planets are large bodies there are many local effects. There can be a local momentary raising of potential by tens of thousands of volts at the point of a lightning strike.
In the same way you will get noise and hum injected into the input of an audio amplifier if you lay out the input (low currrent) and output (high current) earth paths through a common section of track.

Yes a planet will pass a current or a signal according to Ohm's law, like anything else.

But an ideal earth in circuit theory is simply a body that does not change its potential, whatever the current. Planets are usually adequate approximations to this.

 

I remember reading an article in some electronics magazine, about 40 years ago, that referred to something like "Ground Radio". It wasn't about the military's ULF (ultra-low-frequency) ground-based communications system. It was about ordinary people using the ground as a transmission medium, doing things like plugging their guitar amplifier's output into an 8-foot copper ground rod, and other people listening to them from many miles away, using a similar ground rod as an antenna. I don't remember anything more specific. But apparently low-frequency communication is possible over great distances, using the earth as the propagation medium. I'm not sure what carrier frequencies the military uses for their ground-radio network.