Clamping diode between supply and output of an opamp
The role of the diodes is to clamp voltage spikes generated by an inductive load to the supplies.

Your Apex opamp is not an IC, it is made from discrete components soldered onto a metal core PCB. Thus it will not latch-up...

Also, the onboard output transistors already contain beefy clamping diodes because they are MOSFETs.

So, adding extra diodes seems a bit weird, unless they do something the FET body diodes don't.

My first hypothesis would be that this eval board can be used with other power opamps of the same manufacturer, and some of them would have output BJTs instead of FETs, and BJTs would need diodes if used in inductive loads. But in this case, why wouldn't the diodes be on the opamps themselves ?... And the document mentions the eval board being compatible with two power opamps, which both use FETs.

The plot thickens!

Now, on page 3 the eval kit manual says:


  Mount diodes at D1 and D2 and transorbs at D3 and D4 on the “component side” of the board (none supplied) as needed by your application. See Application Note 1 paragraphs 4.3 and 9.1.


...and the appnote says:


  Although most power amplifiers have some kind of internal
  flyback protection diodes, these internal diodes should not
  be counted on to protect the amplifier against sustained high
  frequency, high energy kickback pulses. Many of these diodes
  are intrinsic “epi” diodes that occur as a result of the manufacture
  of the power darlington output transistor. Epi diodes
  generally have slow reverse recovery times and may have large
  forward voltage drops. Under sustained high energy flyback
  conditions, high speed, fast reverse recovery diodes should be
  used from the output of the op amps to the supplies to augment
  the internal diodes. See Figure 16. These fast recovery
  diodes should have reverse recovery times of less than 100
  nanoseconds and for very high frequency energy should be
  under 20 nanoseconds.


So here's your answer: some loads are nasty enough that the FET body diodes can't deal with them, because FET body diodes usually have rather bad specs, and a dedicated diode can be made much better.