Technically they are right. They have nothing to do with India so being called Indian doesn't make sense.

Additionally, the Tamils, Telugus, Malayalees, Punjabis, Sindhis, etc. originated from the country that is now known as India but they also cannot be called as Indians.
The reason for this is that Indian is not an ethnicity. India is just the name of the country given by the British. The name came from the Indus river which forms a small portion of the subcontinent which is now mainly inside Pakistan. North Indians call their country Barath even though the official name is the Republic of India. So, for all intents and purposes being an Indian means being a citizen of India.
Malaysian citizens who are classified as being Indians means that they are a citizen of India, which is of course absurd.

Anyway, from my travels abroad as well as dealing with many expats in Malaysia, I realize that this is a very Malaysian issue due to the chasm of racial and religious divide in our country.

Koreans and Chinese who migrated to France for example, are only identified as French.
A Chinese lady who is a Japanese citizen got really pissed when the local Chinese lady kept asking her where she is from because she has a Chinese name and can speak Mandarin, even when she repeatedly explained to her that she is Japanese.