TX fee is always the burden of the sender so the person who sent you those bits you have the fee was shouldered by him. And if you'll send to someone, you will experience it too as this has been a requirement to make your transaction confirmed.
"TX fee is always the burden of the sender". <<< NOT TRUE.
Again, you're confusing the miner's fee and a transaction fee. The miner's fee (as named) is charged by the miner for confirming the transaction on the blockchain. A transaction fee could be charged by the exchange the two parties are using to facilitate the transaction. It's likely to be two different exchanges for one transaction (one for the sender, and a different one for the receiver). And both exchanges are likely to charge a fee to pay for the service they're providing to either party.
Some exchanges will combine the miner's fee and the transaction fee so the sender or receiver just sees one line item labeled "transaction fee".