Your reasoning is lousy.
I went to a public school in a poor neighborhood, and very well-meaning teachers were trying to give students the tools to break out of poverty. Except for the Asians (who do routinely break out), the kids of most cultural groups were more likely to laugh in the teachers' faces! It was pretty disgusting to watch, really.
In my experience, those who were smart, grabbed every break-out tool that was offered to them, and were lucky enough to stay in decent health throughout their youth, all managed to escape the poverty.
It's true that getting crippled or bedridden in your teens or 20s can make it harder to escape both from prison and from poverty, and that's totally out of your control, but there is plenty that you can actually do to improve your chances, and 99% of young people (that I've seen) did none of it.
Sorry, my analogy is perfectly apt. Your argument was that the fact that there were survivors means there is mobility, but in no way is that reasoning sound. You must compare the number who thrive to the number who don't, or else your methodology is terribly compromised.
Of course, now (but not before) you've started to do that, albeit in the rather unscientific method of, people who know who fit your judgment of certain criteria. There are various other cognitive biases at play here, e.g. fundamental attribution error.
But even if we were to pretend that you, unlike anyone else, could somehow accurately judge the reality of the situation based on your childhood memories, take a look at the criteria you mentioned. You had to include "were lucky enough to stay in decent health" - as if health was merely determined by luck, and not wealth! Access to doctors, medicine, and quality food are not distributed evenly in society.
You, just like me and everyone else, don't have anywhere near the ability to draw reasonable conclusions about class mobility (or lack thereof) as methodological research. But please don't go promoting fallacious thinking by saying things like "the fact that you survived means we have mobility." It means no such thing.
