From college campuses with Indian Student Alliances to Internet web logs called Stuff Indians Like, Indians have demonstrated that to them any person from the subcontinent can be called an Indian. Despite the geographical boundaries that divide Pakistan from Kashmir, Sri Lanka from Tamil Nadu, and Bangladesh from Bengal, Indians see no problem uniting the people from these places under the tri-color banner of India.
This is a peccadillo unique to Indians in America, however. Under no situation or circumstance ever, ever, forever, ever would an Indian in India casually include Pakistanis, Bangladeshis or Sri Lankans in the group defined as "Indian." Depending on your politics and biases, that is either the curse or boon of the motherland. To them history, both ancient and recent, make it impossible to conceive of a totalizing Indian identity that transcends political boundaries.
To Indians in America, however, particularly those of the second generation and beyond, Indian is just easier to say than South Asian. Also, how many Pakistanis, Sri Lankans and Bhutanese cats are you really hanging out with at the University of Florida in Gainesville? If a few then watch out when calling them Indian because at least one is probably Dominican.