Is it impossible in my case? If so, how do others like this one get it?
It's also possible if the transaction has only one output, only the recipient, no change.
You can do that: send an exact amount if you have any unspent output(s) that's a little higher (that can cover the fee) than the amount that you want to send.
But that's less likely to happen.
Disregarding the fiat equivalent, you just have to paste the receiver's address to the blockexplorer and the transaction history below will show the received amount in BTC.