AC MOSFET switching without any diodes? [Low-Cost AC Solid-State Relay With MOSFETs]
In this mode, each MOSFET is on during one half of the wave and the
  other's body diode conducts to complete the circuit.


No that's not true precisely. Both MOSFETs turn-on when the correct gate-source voltage is applied and their respective channels will conduct in either direction of current. Thus, the body diodes are shunted by their respective DS channels: -



The above graph is from here and clearly shows that with reverse DS voltage and current (but still the same positive gate-source voltage) you get nearly identical conduction compared to the forward case.

Clearly, when VGS = 0 the body diode starts to conduct in reverse as seen by the light blue line.

So, I'm sorry to say that the TI person who drew and described that picture is wrong. Both MOSFETs are on and both shunt their respective body diodes no matter what direction current is flowing. I've submitted an error report to TI by the way.