Imastawka covered it completly in his post :

Seems even they don't know their own policies -

Using other programs to address a concern

Buyers can't use more than one resolution method to get a refund.  After selecting a resolution process (eBay Money Back Guarantee, PayPal Buyer Protection, or requesting a chargeback from their payment provider) a buyer is required to use only that process to resolve the transaction issue.

from here  -

http://pages.ebay.com.au/help/policies/money-back-guarantee.html#relationship

So no, she can't close the claim she made through eBay and then file with PP.

And if she can, whoah!! that makes a complete mockery of the policy.

I think you are being taken for a sucker by PP and your buyer.  Stand up to both of them.  

Tell PP that she opened a case with eBay, therefore she cannot open a claim with them.  I don't think it matters that SHE closed the case - the bottom line is that SHE DID OPEN A CASE WITH EBAY - and their policy quite clearly states that she is required to use one process only.