I agree with both of these statements and they aren't mutually exclusive.
Wealthy people are generally those smart/talented enough to benefit from the structure of society. I happen to feel an obligation to help raise the bar in general. Give back to the system that allowed me 'to be', in hippie-speak.
Now, that said, I think those who ask the wealthy to give up their advantages (a la communism) don't understand the value of striving to improve and the power that reward from hard work brings. Why should I work hard if my efforts are just going to go to some Joe who can't be bothered?
I think that those in positions of influence have a duty to
facilitate the ability of others to achieve their own potential. What they do beyond that point is entirely up to them and their own initiative.
Healthcare, education, public infrastructure are the minimal foundations required for a 'free society' who values progress through innovation. Everyone in such a society needs to invest in this basic infrastructure so that those people who can drive things forward are better able to reach their potential.
Who knows how many Einsteins or Newtons have been lost in Africa b/c they died from malnutrition as children?