I tried swapping out the Dell "Model: NPS-250FB B Rev: 00" 250 W power
supply for an Achieve "Model: AX500.N Item: PW606" 500 W supply. No
difference, same memory errors.
Unfortunately, I sort of suspect the Achive supply is a lower quality
unit than the Dell (it feels slightly lighter, despite being rated for
twice the wattage!), but I don't have a known-good high quality power
supply free for testing.
But at any rate, this strongly suggests that the memtest86 errors on
my new Dell box are due to either the memory or the motherboard, not
the power supply unit.