Why should you not turn in the direction of an inoperative engine?
The AvHerald comment is correct, you generally do not want to turn towards the dead engine. The aircraft will tend to turn (both yaw and bank) towards the dead engine due to asymmetric thrust, allowing it to do so at low speed will make it difficult to end the turn, possibly to the point where you lose control. If you turn away from the dead engine, you'll have a tougher time getting into the turn, but the live engine will help you get out of it. That said, attempting low altitude turns with an engine out seems like a bad idea, you should concentrate on going straight and maintaining optimum airspeed to make sure you get some altitude

There are a couple of mnemonics when dealing with engine failures, like "dead foot, dead engine" (determining which engine failed) and "raise the dead" (keep bank towards the live engine)

I can only speculate as to why they chose to go right, either they wanted to avoid the populated area, or they were already unable to control the turn. The high density altitude would certainly affect the OEI performance as well, perhaps luring them into losing airspeed below Vmc.

Disclaimer: I'm not multi engine rated, and have no first hand experience. This is just what I've read.