Alternatively he might not have crashed the car even though he was speeding (and being egocentric against the interests of God, in your words).
We can answer that hypothetical. God completely failed to make me crash my car or injure myself or anybody else in any way. I*n fact, as a result of my stupidity, West Yorkshire County Council will receive a little bit extra income this year which they can use on schools or rubbish disposal or something.
And of course speeding is an entirely subjectively defined parameter - in other words, we as people, via the law define speed limits. It is hard to see how speeding, therefore, somehow fits the criteria for 'sin'.
I would argue that, in the scenario, I endangered nobody. In fact, thinking about it, the camera would have been better placed on the other side of the T-junction from which I had just emerged.