Here is my summary of Rabbi Dr. Tendler’s comments, from a shiur given September 10, 2006. The original is online at YU’s Torah site. (YWN does not permit outside links, even to other Torah sites.) Translations from 1917 JPS (in public domain). All errors are mine.
Exodus 21:18-19.
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And if men contend, and one smite the other with a stone, or with his fist, and he die not, but keep his bed;
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if he rise again, and walk abroad upon his staff, then shall he that smote him be quit; only he shall pay for the loss of his time, and shall cause him to be thoroughly healed.
— This means that we are supposed to get real healing from real doctors, and not just accept illness as God’s will.
Deuteronomy 22:2
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And if thy brother be not nigh unto thee, and thou know him not, then thou shalt bring it home to thy house, and it shall be with thee until thy brother require it, and thou shalt restore it to him.
This means that if someone can heal someone else, one must try to do so.
Leviticus 19:16.
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Thou shalt not go up and down as a talebearer among thy people; neither shalt thou stand idly by the blood of thy neighbour: I am the LORD.
This means that even if you can’t heal the sick person, you must find someone else who can rather than standing idly by — even paying for the healing. In other words, we have to provide healthcare for all!