I'll let the expert accident investigators figure out what happened to the Airbus in Hamburg, while I say some more about the V1 cut. Someone looked at the fact that the engine failure in Vancouver happened only two seconds past V1 and asked, "Isn't there a safety margin?" I have two answers to this.
First the non-specific answer. With airplanes we don't lie about safety. It's not like keeping a couple of steps back from the edge of a cliff to be safe. Every issue in aviation is like keeping one step away from a precipice on each side. You don't increase your margin of safety by taking two steps back from one edge if there's a drop off in the other direction, too. In the climb after takeoff, the narrow path runs between too low a climb rate and too slow to fly. At coffin corner it's between too fast for stability and too slow to fly. With weight and balance every pound I don't put in the airplane is a pound of fuel I won't have in an emergency. And if the manufacturer tells me I have less fuel than I actually do, that doesn't keep me "safe," it forces me to land in a bog when I could have safely gone on to an airport.
Specifically for V1, that is your safety margin. Before V1 is called it is safer to stop. After the call, it is safer to continue. If the runway is extra long, there maybe enough runway to take off even if the failure occurs below V1 and there may be enough runway to stop after V1, but to have the greatest margin of safety, the pilot must follow the drill.
CAI Flight 17 reached V1 at 164 knots. Two point two seconds later there is a loud bang. In those two point two seconds the airplane has accelerated to 170 knots and travelled 500' further down the runway. One point three seconds later, less than the time that it takes me to say "what the hell?" the captain calls reject, and the airplane is travelling at 172 knots, and is 900 feet past the V1 point. Those numbers are from the report I thought I was citing in the first place. (No I don't expect you to read it; it's longer than the other one. The numbers are from Figure 3.)
A runway that is just long enough to stop or go at V1, and no more, is called a barely balanced field. You might think that was an odd coincidence, but it is common to load the airplane and set the power such that the weather conditions will give a barely balanced field length. If the field is more than long enough, it's true that the V1 assigned to pilots could be put in different places. As soon as I say that, someone is going to jump on me for it, because no one wants pilots thinking about it. The correct reaction to an engine failure is hammered into pilots through hours in the simulator. There is an allowance for the reaction time of healthy well-trained pilots to recognize the engine failure and to react and move the controls from full speed ahead to maximum braking. That is already calculated in when determining the V1 speed, so the pilots don't have to think about it. That's important. There are so many things pilots are supposed to think about, but in a V1 cut they are supposed to just act.
I'm cheating on a couple of things here, as the space available to take off in is not always equal to space available to brake in, and different aviation authorities define things like balanced field length slightly differently here, and I'm going to get yelled at if I get very specific. Here's a good definition of V1.
V1 The speed at which, if an engine failure occurs, the distance to continue the take-off to a height of 35 feet will not exceed the usable take-off distance, or the distance to bring the airplane to a full stop will not exceed the accelerate-stop distance available. The engine failure speed V1 must not be less than the ground minimum control speed Vmcg, nor greater than the rotation speed Vr, nor greater than maximum V1 brake energy limit.
The 35 feet reflects other rules guaranteeing adequate obstacle clearance. Note also that it's no good if there is enough runway to take off in, but the airplane can't go straight on one engine because there is inadequate airflow over the rudder to control it. Plus there's not much point having adequate room to brake if your brakes are going to set fire to the airplane. They are likely to get hot enough to blow the tires anyway in an emergency stop.