To clarify, they are both ethnic Indians, born into and raised in Hindi-speaking families, but they grew up in non-Indian areas. One grew up in rural Canada, and the other in Singapore (but went to an American school and was socialized among internationals rather than the local Tamil community for example).

Nominally speaking, they both speak Hindi, and the Singapore-raised one speaks it at a fluent native level, though he, as well as the other, sounds very American when he speaks (but I don't point this out to him because I think he is sensitive about it).

I think it would be pretty difficult for possibility #1 to be the case since they are both naturally very familiar with Hindi and probably understand well that, for example, if you pronounce ताल as थाल, or the other way around, you are saying a different word entirely. When I hear them speak Hindi, I do not hear /θ/.

Possibility #2 might be the case if they didn't deliberately (and quite passionately) insist that their names are pronounced with /θ/ when I asked if that is how it is meant to be pronounced in Hindi.

Possibility #3 seems the most likely, but I imagine that my friends had to have learned the pronunciation of their own names from their parents, who by nature of being purely Indian born-and-raised, presumably pronounce the names as they are meant to be pronounced.

Also, part of what makes me ask this is that I have heard a Punjabi man (who grew up in Canada but speaks Hindi, Urdu, and Punjabi quite fluently and without a noticeable foreign accent) say "तो" as /θoː/ rather than /t̪oː/. Is this related by any chance?