DJ Sam, interesting question, but just because the way you describe it. Also, I think this issues works almost the same way worldwide, not only in India.
Let’s see it step by step.
The duties or taxes from international commerce are usually paid at the moment of import by the “importer” (which is who introduces a product or good to a country which protects its industry or related industries), this you can call it “incoming-duty”. In very few situations the seller/ “exporter” pays because sending a product or good; as a out-going duty.
Now, about the duties/ taxes owner. Its clear, who legally own the amounts collected as international commerce duties/ taxes? That is simple to answer, the government of the receiving country.
But also…
If you use a courier company (as FedEx) for bring a product to you (in your own country) it makes you the “importer” and as importer you must achieve some regulations, conditions AND PAY some given duty/ tax amount, depending on the characteristics and value of the good or product. In this case you are the one who pays TO FedEx (yes you give your money, covering the taxes, TO FedEx) which in this case just acts as a “government’s intermediary” or “government’s representative”, because at the end FedEx will give the exactly amount you pay as “taxes” TO the government.
Of course, FedEx will charge you more than just taxes, that is their business.
I hope you find helpful this answer.
Bst rgds from Mexico.

while taking delivery from custom house you can paythe duty there itself