It means at V1 you need to take the first action to stop or if deciding to go you still have the performance to go. And if deciding to go it means you still should be able to be airborne at the far end taking into account the lower acceleration due to one engine.
Flap config, derate, assumed temp, bleeds, etc are just the variables at hand to get to the point where things work out for a given payload and data to minimize costs wear and maximize payload which i don't see any reason for them not trying to go for at every takeoff
All very good but if you are starting to rotate 5 seconds from the end of the runway with both engines running something has gone wrong.
Also if they did indeeed use an assumed temperature there should have been even more margin. From the sounds of the flight they were carrying out I reckon it is more likely they were using close to max takeoff thrust with little if any flex.