Either way, I disagree that the better people will always prevail, no matter the circumstances. By definition, a stronger candidate will succeed where a weaker will fail, but that will only apply up to a particular challenge differential. If you keep shifting resources to the weaker candidate, the stronger will fail or give up, eventually.
On a personal level, I came from an underprivileged background myself, and succeeded due to stronger drive and working harder than most people I grew up with. But there were many points when I wanted to give up, and I know how close I was to ending up in the same failure mode as they did.
Finally, even if your argument was correct, and these medical school candidates would succeed "regardless", the point of these scholarships is to make sure they choose medicine as the field to apply themselves and succeed in. Sure, they'll be successful regardless: they'll just make a great career in investment banking, and leave medicine for those who have less options.
Society wants great doctors, so it pays the most qualified individuals to undertake a course of training and application in medicine. Makes sense, I think.
This is the "social justice" argument.
Now let me ask you this:
If you get sick and require surgery, would you rather be treated by the smart, skilled, hard-working doctor who succeeded in everything he tried, including being accepted into a top school?
Or maybe you'd prefer the under-privileged doctor, who never did well academically, and only got into a lower-tier school, but managed to graduate thanks to your social justice subsidy?
Your argument seems to make society more just and equal, but you support it because it is convenient to appear as just person, and you are isolated from the repercussions of your proposal. In reality, your policy will prefer and encourage mediocre doctors over excellent ones, you just hope it won't affect you.
Thankfully, American society is structured in such a way that a top school like NYU can muster the funds required for the subsidy, and thus we will have more excellent doctors, instead of more poor ones.