Hi all. I may be a bit late to this thread but it is one of the first that popped up when searching for a solution. Hopefully my experience can help.
My daughter's mid 2013 Macbook Air died. Apple store made no guarantees that any data could be saved IF she decided to send it in for repair for $300.00-$800.00. They also discouraged trying to retrieve the data because it is "not possible"
A USB solution would be the most convenient but USB readers are rare. OWC has one but it's way expensive and a lot of people can't seem to get it to work.
I bought this card on eBay for $8.50 and it worked perfectly in a PC running MacOS (Sorry Apple) Gigabyte Z68 Motherboard
It took couple of weeks to receive the card
http://www.ebay.com/itm/221766582119?_trksid=p2057872.m2749.l2649&ssPageName=STR K%3AMEBIDX%3AIT
This card is available on Amazon (Prime) and appears to be identical... at a higher price:
http://www.amazon.com/gp/product/B00YM462R0?colid=2MA6720D0SE5P&coliid=I31X8N6W8 VY2N7&ref_=wl_it_dp_o_pC_S_ttl
I would imagine it would work the same in a Mac Pro with a free PCIE slot OR a a PC running Linux which can read the Mac file system
Now that the data is safe, time to go back to the Apple store to try to get a firm quote on the repair & decide if it is worth it...
Good luck all. The hardest part was waiting for the card to arrive 🙂