I posted on my experience here over a year ago of a similar MD80 R2-5 relay being put in the airborne mode by a nose gear ground/air sensor sensing air mode because of an over inflated nose gear strut. Taxiing out at night the strobes were flashing, the idle was at approach idle and obviously my takeoff warning systems was inop but at the time I didn't know it. Knowing the strobes turned on with nose strut extention I used aggressive braking to compress the nose gear strut. Strobe lights went out and idle went to ground idle. Also even at the time I didn't know it I got back the take off warning system.
Sounds like the same thing happened to them but during daytime the strobes wouldn't be noticed and they might have missed the higher than normal idle. It would be easy to check though with the FDR. I don't think the crew was totally at fault. As in all accidents, if they are dead, they are the easiest and cheapest way out.
Madrid has a long taxi for takeoff, I had a short taxi at midnight in California so never got a probe overheat.