It's actually very simple.
Speed in and of itself doesn't cause accidents, regardless of what that speed may be. One can be at 0 MPH and be hit by someone else.
What causes accidents is an unexpected or unplanned disruption in a vehicle's velocity, linear or angular, due to hitting something or simply not anticipating or addressing the change properly.
In other words, it's not the motion but the disruption of it.
See also Newton's Second Law.
Put another way, most collisions occur from two distinct objects trying to simultaneously occupy the same space, and that simply doesn't work with motor vehicles.
However, the statement that speed is a factor in the severity of the damage and injury of a crash is entirely true.