This sentence points to a misunderstanding that is common among some immigrants and children of immigrants.
There are HUNDREDS of very good universities in the USA. If you are even remotely competitive for admissions to the highest ranked universities (such as Duke or Brown) then you will get accepted to some very good universities (assuming that you apply).
Also, you do not need to attend a highly ranked university for your bachelor’s degree in order to attend a very good and very highly ranked graduate program (whether medical school or something else). We have lots and lots of direct experience with this in my family. You really can attend a university that is ranked for example in the 100 to 120 range and then still get accepted to a very strong graduate program (even at the level of Ivy League or “top 5 in the world” graduate programs). If you want then I can give you multiple examples where this has happened even in my immediate family (I should probably do this via private message if you are interested).
None of us in my immediate family are MDs. One daughter is a DVM and the required undergraduate premed classes are the same as the required undergraduate pre-vet classes. My other daughter also had a major that overlaps with premed classes. Both knew lots and lots of premed students (at least two of whom are now MDs). One thing that you should know about premed classes (even at a school ranked in the 100+ range). Premed classes are tough. The competition level at Duke or Brown will be intense. The competition in premed classes at U.Mass Amherst will be intense.
Not all students find precisely the same classes tough. For example, some find the required physics and math classes tough. Some find these to be solid A’s that help to offset the B’s in organic chemistry or other classes. However, nearly all students find at least some of the premed classes to be very tough. Medical school is not any easier.
Right now in terms of ever making it to medical school learning how to do well in tough classes is probably more important compared to whether you end up at Duke or Brown or U.Mass Amherst or even U.Mass Lowell or U.Mass Boston.
And really, if you are on track to be full pay at Duke or Brown or pretty much any other private university in the US, make sure that your parents are fine with spending somewhere between $800,000 and $900,000 before they call you “doctor”. This past May my wife and I attended a graduation ceremony where well over 100 people just got called “doctor” for the first time, and the ones who got there with little or no debt were the fortunate ones.