Many buyers want to return, see a "no return" policy and assume they have to have a "reason" for wanting to return. Whether the shoes are authentic or not and whether the buyer really believes they're fake or if they just don't fit or she doesn't like, she's not happy with them.
My advice (and advice I follow myself if confronted with a similar case) is to apologize that she's not happy with them and accept the return.
If she filed a dispute already and claimed that she "doesn't believe they're authentic," you'll have to pay for return shipping and the refund amount will be her entire payment (including shipping).
That way, you'll get the shoes back and will be able to resell them. (Having had a "fake" claim made, you might consider having them professionally authenticated and state it in the future listing. It will add credibility to your listing as well as reassure future buyers that they'll be getting the real deal.)
The problem you can run into should you insist on not taking returns is that in the case of an escalation, ebay will assume that you don't want them back and will allow the buyer to keep the shoes (or destroy them) PLUS issue a refund. You'd be out the money and the shoes.