Sorry Lancer, I disagree. On a maximum weight 747, with maximum crosswind, and a critical engine failure (outboard upwind) at V1, it MAY WELL BE POSSIBLE to remain on the runway.
The directional control issue is more critical at light weights - assuming thrust is not de-rated for takeoff.
At heavy weights V1 will be significantly higher than Vmcg - 25 odd kts. in a jumbo. If an engine fails at a higher V1 less initial yaw will wil be experienced due to the higher directional stability at the higher speed and more control force is available to counteract it.
The most critical situation for directional control is at light weights where V1 = Vmcg. In this case, assuming standard certification parameters, by definition maximum rudder deflection is required to maintain directional control.
Worst case scenario is where the upwind engine fails, in a crosswind, it fails at V1 which happens to = Vmcg, and thrust has not been de-rated for takeoff. In this case insufficent rudder is available to maintain directional control. However, in this case, V1 will be fairly close to Vr and the aircraft should accelerate to Vr quite rapidly due to the light weight.
In short, I believe the directional control is initially more critical in a light aeroplane than a heavy one around V1 but is a problem (on the ground at least) for less time!