"Historically, standard vertical separation was 1,000 feet from the surface to FL290, 2,000 feet from FL290 to FL410 and 4,000 feet above this. This was because the accuracy of the pressure altimeter used in aircraft to determine level decreases with height."
I was trying to point out the reason for the increased vertical seperation at higher altitudes - reduced accuracy of barometric devices at low air pressures (i.e. high altitudes). RVSM was implemented when it was determined that, with the proper equipment and training, it was acceptably safe to have aircraft pass within 1,000 feet of each other at these rarified levels.
Above FL410 the altitudes are at 2,000 foot intervals instead of 1,000, ostensibily for the same reason. (I don't know if the reduced amount of traffic above FL410 played into the decision at all or not.) The valid flight levels are: ...FL390(eastbound), FL400(westbound), FL410(eastbound), FL430(westbound), FL450(eastbound)...