Yes.
The seller is not required to refund unless she is satisfied that there really is a problem.
Normally this means no refund without a return.
Generally it is best to accept that the buyer is unhappy, and let him know that you will send a full refund on the return of the item.
In some cases, the seller will accept a picture as proof that the item is not satisfactory. That's good too.
Don't encourage the buyer to go to Paypal, but follow PP's standard practice. Which is 'no refund without return'.
If PP gets involved you run into potential problems with 'defects' and other problems with your selling account.
Not every transaction will go smoothly. Sometimes the buyer is a scammer or didn't read or off her meds. Sometimes you underpackaged or overdescribed or even shipped the wrong item. It happens.
It's business, not personal.