Are you Indian?

Not a lot of things make me annoyed as much as being asked this question. Not a lot of things brings out the "rude me". Asking this question as a conversation opener is almost guaranteed to make me rude. It is also a source of great amusement to my friends. So why does this question have such an irrational effect on me...
Well to start with I look south Asian - so generally I don't mind an assumption from people who are not from the region, that I may belong to the largest country in the region. Statistically there is a good chance that I am from there. My problem stems from having to insist that I am not from there and still have people refuse to believe it. I am born Sri Lankan, and I cannot link any ancestry back to India (and I can trace back as far as 6 generations). I have also never been there so I have as much local knowledge as can be gained from TV/Internet.
First annoyance started when I moved to Singapore and was required to declare my race. Let's move on from the need to declare a race in this day and age - that is a discussion for another day. I was given the option of Malay, Chinese, Indian or Other. As far as I am concerned Indian is a nationality and not a race. I don't identify with it as my race (whatever that is). So I go for Other and put Sri Lankan as my race seeing as how the other options were nationalities too. I have trouble with officials accepting me as "other" when they see me in person. In fact I have had cases where my form as been "corrected" for me.
Throughout my travels or living and working in other countries, I've had several conversations which have opened with "Are you from India?"/"Are you Indian". When I answer in the negative, it is generally followed by "But you look Indian". So? Another classic "So do you speak Hindi?" - no! "Why not?" - why would I? It is not a language officially spoken in ANY of the countries I have lived in. "But you have a bhindhi/pottu/dot" ... Er yes, I am Hindu/Tamil - neither of which are exclusive to India. Just as much as wearing a headscarf is not exclusive to someone from Pakistan for example. Or being a white caucasian doesn't mean you are from Britain or must speak English.
Why does it make me rude? Often these questions are asked of me by random strangers who are from the region. I have tired of insisting. I am also tired of people from the region who seem to only want to have something to do with me if my answer to the question is yes. Am guilty of generalizing that everyone who asks that question is going to be the same... but having had the formula repeated countless times in countless locations I have grown wary. Next time maybe just talk to me about the weather!