SASless,
The statement he made proves that the safety officer needs to be fired because he is too stupid.
Anyone who understands statistics (that means most of the ppruners below are disqualified) knows that there is no such logic as "statistically, we are due for an accident."
Why? Suppose you tossed a coin that 50 times, and it came up heads 50 times. Is the coin "statistically due" for coming up tails? Absolutely no, since each toss has the same odds (50 - 50) as any other toss.
Another way to see it is to ask the coin where its memory is, the memory that knows how it landed the last 50 times. THE COIN HAS NO MECHANISM TO RECALL WHAT IT DID IN THE PAST. Only humans try to connect the past with the future in that way.
Similarly, the fool/safety officer should know, the actions his crews are taking are succeeding, since they are not having accidents.