Stern vs Cornell non-Dyson for MBB undergrad recruiting

Is it true that NYU Stern is really bad for MBB recruiting? Based on my research, I see that NYU only sends 4-5 students per year to MBB, meaning it's not even a target. However, I see that Cornell has 30+ MBB yearly, and your major does not really matter.

I got into both (Stern and Cornell Public Health) for transfer from McCombs. I thought Stern is a target but looks like only for finance, and Cornell seems to be a target for everything.

Do you know/ can you confirm how many non-Dyson students get into MBB consulting at Cornell vs at Stern for undergrad? 

What did these non business students have to get into consulting/ what qualifications do they look for if not business? Will my health major put me at a disadvantage vs being a business major at Stern?

Even if I'm not a business major, are my MBB chances still higher at Cornell public health? What about PM (product management) odds at Big Tech companies after graduation; would Stern not have an advantage here either over McCombs?

I still wanted to major in business and explore other roles within business outside just consulting/IB like entrepreneurship and PM. However, are my chances still higher from Conrell public health over Stern?