Wire that's rated for 15-amps must have a No. 14 ground and wire rated for 20-amps must have a No. 12 ground. Eldartford, even though you are correct that no current flows through the ground, it's purpose is to act as a secondary path back to the panel in the event of a fault. This is so that the circuit breaker can trip, protecting the faulted circuit. If you cannot reset a breaker, then you have a fault.
I don't know how you determined that the size is 20AWG. Even low voltage control wires are a minimum of 18AWG. Now, if the cable has a metal jacket, then that jacket is the ground and is perfectly ok. The thin wire, in this particular case, would be a bonding wire which completes the connection to the jacket ground. If the jacket is non-metallic, then anything less than 14 wire is not safe and in most jurisdictions illegal.
Check with an electrician or the local building department to be sure.
I don't know how you determined that the size is 20AWG. Even low voltage control wires are a minimum of 18AWG. Now, if the cable has a metal jacket, then that jacket is the ground and is perfectly ok. The thin wire, in this particular case, would be a bonding wire which completes the connection to the jacket ground. If the jacket is non-metallic, then anything less than 14 wire is not safe and in most jurisdictions illegal.
Check with an electrician or the local building department to be sure.