No hospital can turn away a patient who needs healthcare. That is why the hospitals in the border states are in such financial trouble.
As to the education issue, read this:
http://en.wikipedia.org/wiki/Plyler_v._Doe
I believe that is referring to anchor babies.
If this was true, why would the illegal aliens be uneligible for instate tuition at universities, colleges, etc...?
Remember, wikipedia is very unreliable as a resource.