You could be right but now pajeet acts like a bad/troll word (will not say an abusive word as Pajeets literally does not have a sense for that also).
I will make it a little easy for you to understand.
I live and work here in UAE and believe me most of Indians (especially from the South) when asked from where they belong, feel shy and a little embarrassed to tell that they are ''Indians''.
12 years I am here and I have noticed it many many times.
Kerala people go even further and will say ''we are from Kerala''. Like it is the United States of Kerala.
. Only after multiple asking they will tell you that they are ''Indians''. Maybe it is because they are usually well educated and much better mannered than the rest of the Indians and do not want them to associate with the rest of India.
Why do they feel shy? Certainly, India has not earned any good name outside. So you can also troll an Indian by just saying him ''Indian''.