Couldn't wait so read the paper RTFM pointed out..!
We're kind of all right, in a sense, but I conced FFF was "more" right

And wow - the ground station equipment seems far more complex than the receivers! Of course, this is how it should be to keep things lighter and simpler on the airborne side (and perhaps because airborne avionics engineers are simpler too..!?!)
So as I read it:
1) AM is used to modulate the reference carrier, in order to carry voice and morse ident.
2) In a doppler type VOR installation, a pair of of ~10kHz sidebands are frequency & space modulated around the 48 antennas displaced around the array.
3) By being both space and frequency modulated, the doppler effect gives rise to an apparent simple phase modulation at the receiver!
I think....
So, I will still search for a more comprehensive paper, preferably one with diagrams!
Now: maybe I should do some work this afternoon..!
Andy