That is a pretty bold statement. Pretty much all fatal accidents I've heard about involved speeding in some way. Now, anecdotes aren't reliable, so do you have some numbers to back up your claim?
from http://www.motorists.org/speed-limits/faq
Q: Is the National Motorists Association a reliable source for this data?
A: I did the 30 seconds of work to go and Google this, go find your own stats if you don't like mine.
Almost all accidents are "speed related". Very few accidents happen with cars standing still.