First off, unless the wire is less than 20A and protected by a GFCI, he very well should be concerned, this is an illegal installation. It needs to be down at least 24" in most cases for direct burial.

If he wants to put it in a PVC conduit, it wtill needs to be down 18". It's not proper to run UF in conduit except when it needs to be protected from physical damage (such as when it emerges from the ground, by the way that requires sched 80 if you're going to use PVC).

If he wants to run wire in conduit, he should use appropriate wet-rated conductors (such as THWN). Note that yes, running more than 3 current carrying conductors in a conduit requires derating.

Before he guess what is going to be appropriate, someone needs to determine what these loads are (HP of the motor, etc..) exactly.

Apart from proper installation practices, the installation on your neighbor's property seemingly poses no threat to your safety or welfare.
You have been invited to be involved?

120v 20amp circuit. 1/2 HP pump at 10amps. I suppose I have been invited to observe and advise if not necessarily to dig.

As stated, it's an illegal installation. Either bury the cable deeper (24") or add a GFCI and hope it doesn't get dug up, or put a conduit in at 18" (or use rigid metal conduit at 6" but frankly, if you're concerned about hitting it when digging, that won't preclude hitting it, just unlikely to puncture).