Actually the data I've seen states one is way more likely to go from the bottom 20% to the top 20% in many other countries than if you were doing it in the USA.
I'm open to any counter data, but I've read these same numbers in several sources and you can tease it out of my first link.
This effectively defines social mobility as wages being compressed around the median. Small changes in income will create large changes in percentile since it is a relative measure in these cases. For countries where wages are not compressed around the median, like the US, large absolute increases in income produce small increases in percentile.
To put it another way, it is much easier to increase your income in the US but harder to increase your income ranking. I think most people would prefer to have more money than a higher ranking given a choice between the two.
So this is just moving goal posts IMO. End of day it's harder to go from the poorest to the richest. Speaking as someone that was born below the poverty line and but later was earning in the top 1% in the USA, going from sub 14k to 36k was gigantically huge...going from 50k to 250k in as short of a span didnt affect me very much, but moving to France and not worrying about medical bills or insurance companies again was a game changer ... YMMV and everyone is different
To put it another way, it is much easier to increase your income in the US but harder to increase your income ranking. I think most people would prefer to have more money than a higher ranking given a choice between the two.