- The assumption that a helmet certified at x mph is completely useless at (x + 1) mph. I don't have data to back this up, but I doubt that a helmet's effectiveness immediately drops to zero at speeds higher than the certification testing speed. One would expect a declining curve of some sort.
- The assumption that an accident will occur at cruising speed. Most accidents occur at intersections. If the cyclist is braking as he approaches or accelerating from a stop, he is much more likely to be traveling within the speed range of the helmet's certification. A corollary assumption is that the cyclist will not notice a hazardous situation and slow down before reaching it, which is rather unlikely for an attentive rider.
Helmets are not mandatory for Illinois (or Iowa) bicyclists. Each rider is free to evaluate the benefits and risks, then choose accordingly. But if someone tells you not to bother with a helmet just because you ride faster than the speed for which the helmet was certified, don't accept that faulty logic.