To: helmet fire
You have to understand that there are lies, damned lies and statistics.
Here is another point that must be understood. The certification authorities do not use passenger seat KMs or miles. They use hours of accumulated fleet operations. If you will please refer to my post above you will see an example of passenger seat miles being used in the statistics presented by an airline which advertised that they had only one fatal crash while having accumulated 728,400,000,000 passenger seat miles. According to your statistics this is pretty good. However what the airline neglected to inform the traveling public they had only accumulated 98,550 flight hours on their fleet of aircraft in the accumulation of the stated safety figure.
Using your argument above if a person spent his entire life and then some flying in 737s he should never experience a single point failure that resulted in the loss of the aircraft. The FAA dictates that a single point failure in any system that can cause the loss of an aircraft should not occur more frequently in 1,000,000,000 hours of accumulated fleet operations. Or, one time in 114,155 years of fleet operations. Yet, there have been at least two fatal accidents on 737s involving the rudder actuator or the yaw damper in just the last five or six years.
In the first paragraph of you post you stated, "if you were to board a jet aircraft at random every single day, it would be 26,000 years before you were involved in a major crash (this is less than one fatal accident every million flights)"
Using an average flight time of 4 hours you would have accumulated 4,000,000 flight hours collectively on those million flights and the FAA states that no single point failure can occur no more frequently that 1 10 9 flight hours.
Here is a story that describes the thinking and mindset of individuals that quote statistics as if they were the truth.
During the Saturn Apollo Program there was a statistician that worked for North American Rockwell the builders of the Apollo capsule. This man was deathly afraid to fly because he calculated that the probability of their being a bomb on the aircraft was 1 in a million and a half. One day his boss told him that he would have to fly to the Cape and if he refused he would be fired. His colleagues were at the airport when he appeared. They asked him what had changed his mind about flying. He replied that he had calculated to probability of their being two bombs on board the aircraft were 1 in 10 billion so, he was carrying his own bomb.
To put it in understandable terms Jesus Christ roamed this planet approximately 2001 years ago. In hours it comes to 17,528,760. A billion hours equates to 114,155.25 years.
The FAA requires A billion hours and yet no single aircraft model has ever complied with that safety requirement. And, it never will. Even though the requirement is in hours the FAA and other certification authorities will use passenger seat miles or passenger seat kilometers as their justification for airline safety.
The key word here is OBFUSCATION.