Confusing Dual Polarity HV Pulse Generator in AoE 3 X-chapters

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I need a high voltage pulse generator circuit for a simple experiment - testing the pulse-energy endurance of different types of surge protection devices, such as TVS, Thyristor Surge Suppressors (TSS), and Gas Discharge Tubes (GDT). The idea is simple, charge up a capacitor from a DC-DC converter, and dump the current to the load via a MOSFET switch. I found the Art of Electronics, 3rd Edition, X-chapters has exactly what I need. Even better, the section is available at the authors' website. https://x.artofelectronics.net/wp-content/uploads/2019/11/3xp15_HV_pulsers.pdf

The authors' suggested two pulse generator designs for reversible polarity. The first design is straightforward - the MOSFETs are floating and controlled by isolated gate drivers, a mechanical relay connects either the positive or negative HV terminal to the common ground. Thus, you see a positive pulse or a negative pulse with respect to ground.

Later, they also suggested another design with an electronic polarity control. As you see, Q1 or Q2 pushes either the positive or the negative rail to the output. The back-to-back MOSFETs Q3 and Q4 form a bidirectional switch to pull the output back to ground.

Initially I couldn't understand how the common ground is connected. I assumed it's just an electronic version of the previous relay design, and the HV supply can be switched to meet the common ground at either side. But I was baffled because there appears to be no return path at all. For example, if HV is disabled, the output of the two AND gates are false, Q1 and Q2 turn off. I believe the positive pulse capacitor cannot charge up because there's no return to HV-, and the negative pulse capacitor cannot return to HV+ either.

After staring at this circuit for a while, I think I found out the reason: the relay design only requires a positive HV power supply, but the MOSFET design requires a bipolar HV power supply with the mid-point already connected to the common ground. Yet it was not mentioned anywhere in the explanation - a serious omission and it's really confusing. 

But I'm not entirely sure, so I'm posting here for a confirmation. Was my conclusion correct, or did I miss something?