See clip from Attorney Rajiv S. Khanna's conference call video that addresses this question.
Answer is yes. This is the requirement for visa stamping from US. If you want to apply for a US visa, you can actually go to pretty much any country. They are not obliged in that country to take your application but you should. US Consulates don't turn people away no matter you are from which country. They can if they can't verify degrees, for example H-1 visas or they can't verify your family ties in case of tourist and student visas. They can ask you to go to your home country. But there is no harm in asking for an apply. As of right where do you have right to apply, where do you live on the long term basis. Let’s say you are on student visa in Australia, you have right to apply for the US visa from the Australia, in the US Consulate in Australia . Or where you are a citizen, if you are resident in one place and citizen of other you can apply from both places, that's your right.
Everything else is called third country national processing TCM. In TCM almost always Consulate will entertain your application but they may not be able to verify your degrees or your family ties, F-1 visa, H-1 visa, tourist visa this become problematic but you can certainly try. There is no harm in trying. The only time TCM does not work when you are out of status. If you are out of status even for one day, under the law TCM option is taken away, Third country nationals will not be entertained unless you are in extra ordinary circumstances. In practice, however I have seen Consulates don't really make a big deal of out of status; of course unlawful presence is other thing.
So for you Harendra there is absolutely no doubt your wife who is Srilankan citizen but living in India with your parents legally can apply for a visa to the United States, H-4 visa from India.