I've lived in India for five years, and I believe it's better to err on the side of caution here.
It's important to remember that as a foreigner, your immune system is quite differently equipped compared to that of the locals. Indian ground water and tap water is often contaminated with various bacteria, other pathogens, as well as toxic chemicals from agriculture, industry, etc. The most common and most reliable way to truly remove all of this is a quality system of Reverse Osmosis (RO), preferably with ozonization or UV for redundancy. This system also needs regular maintenance and quality control, and the membrane has to be replaced regularly. Anything they give you in a restaurant or hotel that is referred to as "filtered water" or even "RO water" may or may not have been produced according to such standards. Or some employee may have washed a vessel with tap water before filling it with this water, etc, etc. In some cases it may be satisfactory for the immune system of most locals, but not for that of a foreigner.
For drinking water, stay away from all fountains, taps, non-sealed and non-branded vessels , and the like. I would stick to this advice even in the airport and at hotels. Also use bottled water for brushing your teeth.
Buy bottled water of a known brand. (Bisleri, Aquafina, Kinley.) It's preferable to get them from a large supermarket or other trusted source, to avoid counterfeit bottles. Your hotel will probably sell them. Make sure the caps are sealed. You can typically get 5L or even 10L bottles. If you do this, though, make sure you don't get the type where the same bottles are reused, as the refilling process can often be unhygenic. Below is a picture of reusable bottles that you want to avoid. They feature quite sturdy plastic. These are 20L, but smaller varieties and shapes also exist.
If they ask for a deposit on the bottle, and the bottle is exchanged back for another bottle after use, then you know you're dealing with reusable bottles. Some of my friends have had water tests done of the reusable bottles (of a known brand) and found that they are more likely to contain various bacteria. The tests of the disposable bottles, on the other hand, turned out fine. If there is no deposit on the bottle, then you know that each bottle is new.
Stay away from reusable bottles, even from known brands. Any local refilling facility may or may not have their procedures in place. These bottles may in some cases be washed with tap water between use, or even not washed at all.
Here is an example of a disposable bottle (which is what you do want) from a trusted brand:
This bottled water is quite cheap here. A 1L bottle costs €0.26. A 5L bottle costs €0.87.
Personally, I have my own RO system, UV filter and ozonizer, but that's usually not an option for short-term visitors.
Since most of the bottled water here is RO processed, it's good to choose a type that has added minerals in it (Bisleri, Kinley). The RO process removes all bacteria and harmful chemicals from the water, but it also removes all the useful minerals.
For those concerned with the environmental impact of using plastic bottles, you can make sure the plastic is recycled (as opposed to ending up burned or dumped in a field somewhere). In India, there are people who collect plastic for a living in order to sell it for recycling. You could give it to those workers, perhaps along with a tip, as such people are typically poor.
Other than that, if you're worried about the plastic, then the only real and safe option that removes both pathogens and toxins is some sort of RO system, but for a short trip you'd have to consider if the environmental footprint of buying a whole system is really smaller than some plastic bottles.