damage a relay by crossing meter leads?

EXACTLY! Therefore it is 0V. +12V & -12V means a 24V supply. Battery neg, but neg what? neg-0, neg 12? Look at amplifier rails, they are a + & - voltage rail/bus with a nominal earth/ground/common at zero Volts... But I blame those Audio dudes. Until then, I was quite happy with +12 & -12 meaning the 12V battery terminals. (Actually the change came with the flooding of Op-Amps onto the market about 2 score years ago.) Besides, be fair - I need to be reasonably correct once in a while....

I'm lost here, isn't 0v what I suggested earlier?

I thought you wrote "0v return? Not physically correct unless quantum theory has changed but effectively so." and later "The quick answer is -12v...." (but you continued "... but then we don't have 24 volt batteries!" which IMO is what I said, namely that to use +12V & -12V means a 24V power supply. So we are agreed, the correct labeling is +12V and 0V. Call 0V what you want - chassis (even if floating), ground or earth (despite having rubber tyres in between), or return.