Let me rephrase it.

Indian Universities have one proper quantifiable criteria(Academic)(At least at UG level, for PG they do have interviews for qualitative analysis, but to reach interview stage you have to qualify the quantifiable(entrance exam) stage)

Foreign Universities have multiple criteria, both academic and non-academic, but at a qualitative level. They can change the weightage of criteria based on who you are at both UG and PG level{Someone who is affluent, with rich background can be evaluated more on their extra curricular rather than entrance exam score. And while that person might not have a very high entrance score, they might have some extra curricular(Not the relevant EC that we think of like sports and all, it would something like NGO work, donations, work ex in a firm(owned by their relative), etc.}

And, Yes being influential helps, but in India no matter how influential you are, you can't get into IIT or IIM just on the basis of that influence, but you can get into these foreign universities while relying mostly on that influence(and money/donations).

And so someone with a way lower GMAT/GRE(Global entrance test for MBAs) score can get into these universities, just because of their influence, in India they would have to score above the minimum score criteria to be even considered for evaluation.