Ever heard of IIT? Probably the best engineering school on Earth, and IIT grads are some of the world’s biggest movers and shakers. IIT applicants who can’t quite make the cut frequently end up at MIT and Stanford.
Actually it is the other way around. If they can’t make it at Stanford/Cornell/MIT, there is a good chance of getting in at IIT. One advantage IIT has, from the corporate viewpoint, is that IIT teaches more directly to application. Not much theory is taught. While this allows the graduate to apply the knowledge quicker, it also hinders them later if they move into strict R&D. That being said, teaching direct to application allows an educated workforce who are desired by companies looking to relocate parts of their operations to cheaper locales (part of why IIT was formed in the first place). Several IIT graduates actually do follow on to higher education at Standford/Cornell/MIT.
NOTE: By ‘educated workforce’, I don’t mean corporate drones. The top graduates have very similar qualities to top graduates of U.S. undergraduate colleges (which is why they can transfer to Standford/Cornell/MIT for graduate studies).
Effectively IIT makes a good undergrad college for Indian nationals, allowing transfer to Standford/Cornell/MIT for graduate studies.