You are very wrong. Being in a foreign country, these NRIs miss their homeland so much that they donate at the drop of a hat, forget about any major calamities. It is just that people are not properly informed of their activities. Every dropof blood shed in India of any fellow countryman hurts them more than it hurts Indians, so t is only logical that they care for the people back at home. May be some NGOs take advantage of their kindness and help themselves instead of giving it away to people for whom the help was sent.
Hope the above comments clears your ideas some and also of all teh Indians who have this misconception. That apart, the remittances not only helps GOI but also the family members who live in foreign countries.
