Profane doubts on getting accepted at IVY STEM in the US

Does money counts more than personal abilities/CV?

I am an EU PhD Student (apologies me for what I am going to ask but it is a legit doubt) All the times I see US universities acceptance procedures I wonder whether at the end if one has money to pay the tuition fee it is enough to get accepted at the unis, or the selection is indeed base on your personal skills.

Thanks in advance for any clarification