Having read most of the online references to this circuit and performed some simulations, I still don't have a firm grasp on how this circuit functions.
and here is one of the better intuitive explanations (in my opinion) of how the circuit works.
If you simulate this circuit and make a tight coupling between the primary and secondary of the "transformer", the circuit will not work as expected. If the coupling is tight, the top of the secondary will be in-phase with the primary, as you would expect. But, as the explanation above describes it, you want the secondary windings acting like inductors so that there is a 90 degree phase shift at the top and bottom of the secondary with respect to the centre tap (at the resonant frequency).
So, if my understanding is correct and the secondary winding halves are acting like inductors to the current arriving from the top of the primary tank (via C at RF) why does this circuit need transformer coupling at all?
Anybody care to confirm or reject my speculation in the comment section? Anybody - sob!