EFATO at Vr
The Emerald Airways accident at STN is interesting comparison. The crew actions were praised by AAIB although they contravened OPS procedures. Similarly, AAIB report 1/2001 ( I think) Cessna 404 Titan at Glasgow which resulted in fatalities was potentially as a result of crew following standard operating procedure - to complete a circuit and land after single engine failure.
( In fact it was finally concluded that the wrong engine was shut down - leaving the aircraft without power after failure at or just after Vr.)
Indeed, that aircraft would also have been capable of flight subject to reduced climb performance. It was close to MTOW and perhaps had the crew elected to land ahead initially, they may have managed a landing outwith the airport boundary.
It seems at Madrid there was catastrophic engine failure at a critical point. If the crew decided to try and land ahead I expect they had a very good reason for making that decision. Engine failure at close to MTOW when hot and relatively high is never easy. Add potential hydraulic leakage/pressure failure due to a breached pipe and resulting in control authority issues and then there may be even less hope of continuing a climb and return.
The evidence suggests the aircraft was airborne- but only just. Without a positive rate of climb and with perhaps some runway and overshoot ahead it might be seen as a reaosnable option to try and set down rather than continuing. TORA at Madrid relative to Aircraft MTOW and TODR would perhaps leave a margin of which the crew would have perhaps subconsciuosly been aware or could see. Not being proficient on MD80 I can only speculate as to the view ahead after Vr and initial climb.
I think the crew may well have made the right call.
If the port engine had an explosive failure then it would seem strange that the aircraft would then veer off to starboard. The loss of an engine alone should not result in a huge turning force given the engines on MD80 are relatively close to the centreline. However, reverse thrust on the starboard side only would establish a positive turning moment which would be difficult to balance with rudder ( assuming that the hydraulics had not been fatally damaged). If the port clamshell was inop ( liklely) or if there was no thrust available anyway on the port side. Then would this be enough to slew the aircraft off the airfield?
All the above is pure speculation for which I should offer some apology. However, in circumstances it is inevitable that the crew's actions will be criticised by some. My point is that they will have done everything that they were trained to do to save the passengers. They made the best decisions at the time based on the information at their disposal. Sometimes that makes no difference to the outcome.