"Desi" is a term that refers to a person of South Asian origin, primarily from Pakistan, Bangladesh, India, Nepal, and Sri Lanka. It comes from a Sanskrit word that means "homeland".
NRI means "non-resident Indian". It is a term that applies to those of Indian origin that live in other countries (emigres).
I am interested to know how in some articles they found out if Dr. M-P traveled to India. I'm a US citizen with a PIO (Person of Indian Origin) passport, which means I'm entitled to leave the US without having to go through the visa process enter India. If Dr. M-P is a US citizen, I think that she, like my parents, also has a PIO passport and would therefore be more difficult to trace because there's only a record of her passports and not a visa application process.