IIT tougher than MIT/Harvard? You are kidding..

In India I used to hear everyone saying( and all the media hype surrounding it) that it is tougher to get through IIT than even Harvard/ MIT. This is said mainly on the premise that the acceptance rate( the number of students who apply vs those who get through ) is lower for IIT than for the others. Lets explore the reasons why this isn't true:
1. Everyone remotely connected with science in India gives the IIT exam. If you have taken Maths in class 12 it goes without saying that you will be sitting( or your parents will coerce you into sitting) for the exam. No one just applies to Harvard or MIT, it is not a by default phenomenon.
2. You apply individually to Harvard/ MIT and it is not a joint entrance examination. I know quite a few people who apply to some really good colleges but not to MIT because they feel they aren't good enough to get through. I have never heard anyone saying I they won't be giving the IIT exam because they aren't good enough, people just give it.
3.The cost of attending Harvard is so much more than attending IIT. There are people who don't think of attending such schools solely because of the cost and never apply. Never happens with IIT.

IIT is tough to get through but I am pretty skeptical whether it is tougher than Harvard/ MIT.