If you relax the constraint a bit and replace top 1% with top 5%, then almost 40% of Americans will make it at some point. And 12% of them will hit the top 1%.
Cool follow up link, however it distinguishes between the difficulty of reaching the 1%/5%/etc. for a single year vs. sustaining this state. I'd argue the concept of "being one of the 1%" implies being able to sustain this level for longer than a year.