Once people have high SAT/ACT scores, the deciding factor is not a few percentage points; and more than 9 out of 10 will be rejected, no matter what. At that point the overall application will decide which students make up a geographically, socially and otherwise diverse class. Many factors are being looked at - and a high SAT/ACT score will not automatically compensate for a less-than-stellar GPA, or the mix of honors vs. AP rigor, per example. But even if all numbers are high and someone is in the top 10% of their class - there aren’t enough spots for 90% of applicants!
So - it’s okay to aim for the stars, so that you (and your parents) don’t forever wonder “what if”. But as far as the importance of an Ivy-League college to your potential medical career (which very possibly will happen at a completely different University than your college), your parents are completely misinformed.
If anything it will be your medical school (grad school) that people would take note of once you are a doctor, NOT where you went to college 6 or more years prior.