Gaining speed for a car collision

It is said that if a (non-frontal) collision with another car appears imminent and unavoidable, then the wisest course of action is to "put the petal to the metal" for maximum speed. The myth mostly concerns collisions at intersections typically at angles of 90 degrees.

The idea is that while the increased speed does in fact cause more damage, it also increases your inertia (resistance to a change in velocity) and thus yields the smallest accelerations and decelerations from an impact with a car of a constant mass and velocity. As we all know, survivability is a strong factor of acceleration/deceleration.

Would you test this myth to determine if faster collision speeds in non-frontal collisions with automobiles are actually safer for those in the faster car? It is obviously more dangerous for those people in the slower car, but then again, the myth only concerns the safety of the occupants of the primary vehicle.

Momentum (p = m*v) is a function of velocity too, but faster speeds may not mean more collisions, because the path will be less prone to deflection. The scenario of most interest is that you are traveling through an intersection and you see a car coming at you from the side (perhaps running a red light) like from a side street at an intersection (seemingly out of nowhere).

This happened to me once when a car (facing me and in the intersection) made a left turn on my green and hit the driver's door. Stopped him cold and spun his car 90 degrees counter-clockwise, but my car (about 45 mph) hardly deflected at all and I retained complete control as I braked to a full stop. I think that this myth might be true. In general, the fast you are going the better it is for you.

BTW, on the damage from the kinetic energy, your car will absorb the damage and spread it out over a larger area with higher speeds. Additionally, with more momentum, there is less deceleration, thus the faster vehicle incurs a smaller change in velocity. It thus absorbs less kinetic energy damage than it might otherwise be expected to absorb in any given high speed collision (assuming no collisions with immovable objects or flights off of very high cliffs, etc.).