If you look at the aggregates, sure... But that's also ignoring the fact that the addition of the low skill population makes both the high skill workers better off, but the low skill workers will be better off than they were from where they came from (if it's truly because of economic opportunity, which it is in this case.)

Your entire post was predicated on the premise that aggregate measures of a single country accurately reflect the real income mobility of the members of the population, so it's not just the quote that I took from you here. The premise is faulty, and your argument just doesn't stand.