Skills? Not necessarily, but there's something a lot of immigrants possess that your university graduates don't: freedom from the weight of student loans.
I'm not from India, so I can't speak for them. Plus, I imagine that the situation in India changed over the years and it's probably not the same as when this trend started. But I can speak for myself and people I know from many other countries, including China. Most of us have had an education that is on par with a lot of American colleges and universities, but without the crushing cost.
Get rid of all immigrant workers and the industry will collapse, because your graduates need to pay off a huge debt that immigrants don't have.