If the bottle arrived with the cap broken, then the item was 'not as described' and the buyer was perfectly entitled to a refund.
For the money paid, the buyer would expect a perfect item.
They only bought the perfume a week or so ago so can't have used a huge amount.
"There are two ways to be fooled. One is to believe what isn't true; the other is to refuse to believe what is true.”
Søren Kierkegaard, Danish philosopher (1813 - 1855)