Ouch. Sounds like the FO was trying to do the right thing while the Captain didn't react correctly. While it could have been possible to get an overspeed during the climb as there were reports of turbulence while over mountainous terrain, the combination of overspeed on one side in combination with reports of icing conditions make wrong airspeed indication due to pitot icing more likely. Pulling engines to idle while continuing to climb would not be the right reaction even if there was an overspeed. Subsequently ignoring stall warnings and stick pushers while at least some of the airspeed indications seemed to be correct (Comperator warning) until the engines flamed out is just not excusable. Much more realistic training is required to prevent these things from happening.