How does this phantom-power receiver actually work?
Your analysis is good so far.

Understand that the phantom power source is effectively 48V with a source impedance of 3.4 kilohms, so the voltage on Q1,Q2 collectors is strongly dependent on the load current. 

This circuit will work as intended provided the load current is somewhere around 10mA (dependent on the gains of the transistors, since the base currents are of the same order as current in R3).

Coincidentally, 10mA is quite a good current for a low noise JFET (2N5459 for example) somewhere off on the left, to operate at its lowest noise figure - though I have my doubts about the TL072's noise contribution.

You and Andy are correct that a Zener is an alternate way to provide voltage stabilisation, though when you come to measure the resulting circuit's performance, you may find (as I did in similar circumstances) that its dual role as a noise generator is difficult to overlook.
Note that zeners around the 10-12V range (and higher) are technically avalanche diodes, and quite noisy

IMO this circuit is quite cunning in overcoming that problem and providing "just good enough" voltage regulation without that unnecessary issue.