That's not strictly true. It all depends on the cut of garment, the fabric used, & what you're doing & where.
I am a pale-skinned strawberry blonde & suffer a lot in the heat - to the point where I only holiday in hotter countries during their spring/autumn/winter. I often wear dark colours, as they're more practical than pale ones when you're travelling around. I like cotton/linen/viscose/silk in open airy weaves like gauze or cheesecloth.
The key is to wear loose clothing - if you're wearing a tight black T-shirt & leggings, then yes, they'll absorb heat quickly & trap it next to the skin. Plus tight fabric around the armpits & crotch collects sweat more. And so you'll be horribly hot & sweaty.
However, loose black garments allow the air gap between the fabric and skin to create what's known as a "chimney effect". The heat absorbed by the fabric escapes into the air before it reaches your skin. Black fabric is also an excellent radiator of heat. When you sweat, the moisture evaporates faster than in white/pale clothing, & cools the body. It's why Bedouins wear loose black robes in the desert.
Even if I was on a city break rather than travelling around India, I would wear dark as well as light clothing, & focus more on the cut & fabric of what I was wearing, rather than the colour.
If the OP is walking around lots in the heat of the day (unwise, & I doubt she will), white will be very effective at reflecting heat before it's absorbed by the skin. But if she's indoors/in the shade a lot, wearing loose dark clothing will actually radiate heat away from the body faster than pale clothing.
There is also, for me, the mess factor!! If I was meeting a wealthy work colleague for lunch in Milan, I would worry about wearing a head-to-toe white outfit. To the point where it would probably affect what I ordered from the menu!! Tomato sauces, oily salad dressings ... all that potential for splattering food over myself! The embarrassment ...!!! 😬