That's weird, the only thing that I know that can burn a resistor is excessive current, the fact that you reverse the polarity should not be the cause...Oh well...
Yes, by no means do I disagree with you,
@phi1 and
@EGRENIER.
What I was describing was the evidence (the effect of the reversed power), not the cause.
I surmise that the resistors blew because the reverse current was drawn so that a component designed for -12 was forced to operate at +12. As
@phi1 said, '... some other downstream component shorted power to gnd after the resistors.' Maybe it was the 7805 which blew and sent reverse voltage to the rails though the 10Rs thereby*. The microprocessor died as well as you'd expect, so I ordered a replacement board and chip for later.
*I revisited the docs: "Power Supply: Here we see footprints for two different types of power connectors. The Positive and negative voltage rails go through 10 ohm resistors and are then filtered by 10uf caps, and .01uf caps on the pins of the op amp. The positive rail is then sent to a 7805 voltage regulator which provides +5V reference voltage for the microcontroller." The PSU section of the circuit contains no diodes.
I managed to build a successful replacement later
_ sound happy ending chord here_,
but most importantly I highly value your responses (and interest).
Thanks for taking the time and trouble to discuss this. I learn as I go and this was great food for thought about design quirks.