Whether that is the way it should be or will be in the future is another kettle of fish. Whether that answer will make people upset is also a good question. It looks like Google is taking advantage of the Internet to try to tell everyone what they want to hear.
But right now if you want to take an international flight there you'll need a visa from India. So it is part of India.
What's different about Tibet? China claims Tibet is a legitimate part of its territory, but others claim that China is an illegal occupier. However, at least for now, Tibet is a part of China.
Greece claims Cyprus is part of Greece, whereas if you look on a map your guess would by Syria. The Turks think it is part of Turkey.
There are lots of places like this in the world. The CIA world factbook has a section 'border disputes' for almost every country.
Also, I'm not exactly sure how it's any more "part of India" than it is "part of China". Says who?