Self-selecting out is true for IITs also. Let's not forget that IITs are focused purely on engineering stream and a bit on technology management courses. IVY Leagues on the other hand are broader universities covering other streams such as liberal arts, life sciences, law etc.
If you compare the size of student-body which grows up each year (the ones qualifying 10+2 intermediate school) in India, and the fact that only a fraction of it applies and appears for the IIT entrance, you will get a clear comparison on which university has the lowest acceptance rate going by this metric too.
However, let's not blind ourselves with ratios and percentages alone because absolute numbers have a bearing on competitiveness too.
I remember there was a study a few years ago suggesting that countries like India and China are so populous that the number of honor kids they produce is higher than the number of kids we have in west [1]. Also check out this video which shows how IVY leagues form a backup option for most IITians with Vinod Khosla, Narayan Murthy et al.
http://www.youtube.com/watch?v=BK3rX1sg5kg
Not saying that universities like Harvard do not have a high enough benchmark or a lesser quality admission process, but if we were to compare quality of entrance exam/criteria of only the engineering streams of Ivy Leagues/others universities with what the IITs have, then the latter would be right on top.
[Disclosure: I am an IITian, so apologies for the conflict of interest w.r.t to my statements above.]
[1] http://blogs.wsj.com/speakeasy/2012/06/26/are-your-kids-smar...
Till 2012, AIEEE was the other most important entrance exam in India and it was the basis for admission to all national colleges other than IIT. ~1,100,000 students applied for it compared to ~500,000 who applied for IIT
Source: http://articles.timesofindia.indiatimes.com/2012-04-28/entra...
I am NOT saying that the IIT admission process is easy, but I will say that this is the wrong way to show that the process is hard. Not all smart students vie to attend Harvard, MIT, and Stanford in quite the same way that many, many, many smart students vie to attend IIT. The base of applications is broader, by far, for IIT, partly because of the especially steep drop-off in quality and in prestige from the IIT echelon of universities in India to other universities. If we compared Harvard's number of admitted students in the most recent reported year, 2,029,
http://news.harvard.edu/gazette/story/2013/03/college-admits...
to the number of students who took the SAT college entrance test in the relevant high school graduation class, 1,664,479 students,
http://media.collegeboard.com/digitalServices/pdf/research/T...
we could calculate that 0.12 percent of all high school seniors in the United States who took a college entrance test were admitted to Harvard, quite a low base admission rate. The key, of course, is that many American students self-select out of applying to Harvard, and indeed don't self-select to submit an application to any "prestige" university.
That said, direct examination of the IIT examination item content
http://www.askiitians.com/iit-papers/iit-jee-papers.aspx
may suggest what level of performance on specific item content is necessary to be part of the small subset of the large number of IIT joint entrance examination test-takers who gain admission to an IIT campus. On that basis, I agree with the statement that the IIT undergraduate programs are highly selective and likely to collect on one campus many very smart young people who provide a good peer group to one another so that everyone on campus picks up habits of aiming high intellectually, as the IIT alumni I know here in Minnesota all seem to do.