From the scope picture it looks like the signal level from the radio is 3.3V and the pulses are 1500 microseconds wide ('control in the middle of the 1000 to 2000 range'). You should be getting 1500 microseconds displayed for both pulseIn() values.
How long is it between lines appearing on Serial Monitor? The default timeout for pulseIn() is one second (1 million microseconds) so it should be about two seconds between lines with no input signals.
Do you have the Arduino Ground connected to the Radio Receiver Ground?