What explains this puzzling radio signature from a fireball?
I checked with the people who run the BRAMS project and they confirmed my reasoning, and added another possible explanation.

Even if the fireball moves away from the receiver AND transmitter, the ionization trail it leaves behind can expand and be blown by mesospheric winds towards the receiver and/or transmitter. It's this trail that mostly reflects the radio waves.

And theoretically it's still possible but unlikely that the observed Doppler signal was coming from another meteor trail unrelated to this particular fireball, but coinciding with the exact time frame the fireball appeared in.