hbs, let me share my experiences with HSW with respect to Indians (mostly IITians) based on my discussion with my friends in those schools.
guy 1: IIT - McK and then corporate strategy in Europe. He got into H S and dinged at W. 780 GMAT and he has solid extra curriculars. So, he does not have any 'out of the world' experiences but just solid experiences all the way through.
guy 2: IIT and in R1, he was rejected in all his schools. R2, apped to S and a couple more, got into S. Again, solid experiences, nothing spectacular.
guy 3: IIT, worked in the US for a financial services firm, went back to India to start a non-profit and got into H.
guy 4: IIT, worked in the US for a financial services firm, HBS
Girl 1: UG in India and a top school in Europe. Experience in big-3 MC and now at HBS.
So I dont think there is a magic formula to get into HS but I believe that 'solid' experiences with some good Ec's will atleast get your app a look. Or, you need to do something 'out' there. Especially Indians- every desi applicant I know throws in an app to H or W, sort of like a hail mary. I also tend to believe to some extent that pedigree matters to those schools.
Having said that, while I am not saying that it is easy to get into HBS but it is not as difficult as the stats seem to indicate just because of the hail mary's.