Difficult to know exactly here, without details of whether/when an ebay case was opened and how the refund was paid - a full refund was given, but then a partial refund was agreed? I wonder if the buyer contacted you to ask for a refund but didn't actually open an ebay dispute case? In which case the error was to refund without an ebay case being open as mk one said.
Basically how it should work is the buyer opens a dispute, you either accept the return or agree a partial refund to close the case (if the buyer agrees), then ebay charges you for the return tracked postage, and only when it arrives does the buyer receive the refund. If you didn't go through that process for the refund ebay are unlikely to be able to help you. If all the payments were done through Paypal then they may be able to advise if you call (I've found Paypal quite good on the phone, but like ebay they'll only work to their procedures so they might tell you they can't do anything if you chose to refund the buyer without having received the returned item).
It is true that the buyer is always right on ebay. Basically in any ebay sale the buyer can say whatever they want - truthful, bizarre, subjective, whatever - about the condition of what they received and the system will 'decide' automatically in their favour. Some sellers get very frustrated by this and complain furiously that what they sold was correctly described, the buyer is lying/taking the proverbial, etc. But if you sell anything on ebay it's really best not to let that bother you since there's absolutely nothing you can do about it, it's just how ebay works: no-one in ebay HQ is making decisions on whether a buyer is trying their luck, trying to pull a fast one, etc, so there's no point protesting: for any 'item not as described' claim the seller must accept the return, pay for the return postage, as well as losing the original postage costs they paid. It's a very useful policy for buying but very risky for selling anything you can't afford to lose. As a seller you just have to put up with the possibility of coming up with the occasional fraudster or just do collection and cash only, which is what I tend to do nowadays for anything much over £100.