Something that doubles or reduces by 10x the random probability is not "closer to random". I doubt that if you tell something that a factor is "closer to random than to a perfect predictor" they'd expect something like that.
> You say "should" but it seems like this is only true if you expect (and want) completely random results.
There is quite a lot of randomness involved in where one ends up. There is a random distribution of ability, of work industry, location, country, luck, connections, timings... quite a lot of factors so that you'd expect that randomness to dominate over the whole population and things be close to ~20%. In fact, countries with higher social mobility tend to be fairly close to that 20%. In Spain (which is by no means the best at social mobility, but it's the only one I have data at hand from) we are pretty far from that 43% chance of staying at the lower quintile, and also far from the 3% of moving from bottom to top: https://widgets.elpais.com/mapbox/2020/07/atlas-renta/pc_nac...
This shouldn't be a matter of what the layman thinks, it is a question of statistics. If someone said or thought that the class you were born into has a bigger impact on outcomes than other factors, they would be wrong.
Can you check your link, as it has no text.
>you can rephrase the statistic in another way, such as saying that 13% of the people at the lowest quintile should be in the highest income bracket, but they're not there because they started poor.
You say "should" but it seems like this is only true if you expect (and want) completely random results.