My inclination would be to refund immediately, because there are really 3 potential issues at stake:
1) Defect from open case; If you allow the buyer to open a case first, you will get a defect if the buyer chooses the option "received item that does not match the seller's description", or "item received is not as described", etc. (i.e. broken item). According to the Spring 2014 Seller Update, you will get this defect regardless of whether you then refund;
2) Possibility of an open case being escalated and closed by eBay: This is less likely, but could happen if the buyer opens a case, escalates before you have a chance to refund, and eBay/Paypal step in and refund directly. As you probably know, these are counted separately and in addition to defects, and would go against your 0.3% allowable rate of closed cases without resolution.
3) Defect due to buyer FB/DSRs: There is a risk that a buyer who has to open a case, even if he/she is then quickly refunded by the seller, may be tempted to express their dissatisfaction by leaving neutral/negative FB or low DSR ratings.
Although you would only get 1 "defective" transaction as a result of #1) and #3) above, even if all the possible defect-producing factors were in play, the problem is that the defect could come from any one of those various sources. The other problem is that we sellers have to worry about our total defect rate (2% for TRS, 5% otherwise), and the DSR average (4.6%) for PowerSellers. While eBay did make it clear that multiple defects will only be counted once toward a given transaction, it's never really been clear to me how the percentage rate itself impacts overall seller status.
I would say the scenario least likely to produce a defect (although not guaranteed - the buyer could still leave neutral/neg FB or low DSRs) would be an immediate, cheerful refund. My approach in such a situation is to be quick to act, apologetic, and do my best to make the buyer satisfied with good service despite the disappointment. You might even consider, say, sending a voucher for 20% off the next purchase, or an eBay gift card? It really depends upon how critical avoiding a defect is for you.
All just my own view of it -- others may differ, but best of luck! 
