If you're very poor, but smart, america probably offers more opportunities than most euro places. Elite Unis heavily subsidize in this case.
The more common case though, is somewhat poor (single mom, 3 siblings, $40,000 a year), and somewhat smart but not national merit level. Many people in this situation seem to wind up getting aid packages with low interest, but huge principal, managing to get their degree but graduating with a lot of debt. This may be changing with even the shift to free tuition by some elite unis, but haven't seen really big changes yet.
In your last sentence, you seem to make the same point, only for med care rather than education.
So perhaps we agree that the american system is harshest on people who are poor but not "poverty level."
That is a bad way to be though. Because what happens when you are poverety level, and work your ass off to get up to the "just poor" level? You lose all that subsidy! And back to poverty level, for many.
(Not that I'm saying our medicare/medicaid/emergency system isn't somewhat broken. For example, many people who qualify have not filled out the necessary paperwork to join. The problem with lack of medical coverage, though, is much less with the indigent than it is with those just over the poverty line.)