I'm not sure if everyone survives IIT by rote memory. I'm sure some people thrive by truly understanding the fundamentals. For those who want to really learn a hard subject, IIT is wonderful. On the other hand, I have a hard time imagining anyone could survive a STEM subject through mere rote memory. A STEM subject is built on layers and layers of abstraction anyway. If someone could use things like "any subgroup of a commutative group is normal" or things like BPP=co-BPP to solve problems via sheer rote memory, what can I say? Hmm... Kudos?

Seriously, though, we should look at statistics instead of individual samples to assess the value of education. I mean, how many students can really solve a JEE question like below by rote memory? I'm sure there are some who got lucky, but I'd rather believe most of the students who could solve such problem truly learned some math:

If f(x) is a differentiable function and g(x) is a double differentiable function such that |f(x)| <= 1 and f'(x) = g(x). If f^2(0) + g^2(x) = 9. Prove that there exists some c \in (-3, 3) such that g(c)g"(c) < 0.