Sounds like something that can happen when someone doesn't have an up-to-date version of Flash, except for the part where they refresh. But do you mean it randomly shows either the Flash/Flex version? IOW is the refresh simply causing the other (Flash) version to display?
@Ansury, no I am sure it is the same one after you refresh, it uses a cookie and keeps showing you the same one once you have seen one. Also I watched it happen on a co-workers computer, and it was the same main version that loaded correctly after refresh. (they are easy to tell apart, especially since I made both). He was on Flash Player 10.