I had the exact same problem. My Mid-2013 MBA suffered severe water damage and the logic board is fried. I plan on having Apple send it off to have the innards replaced (which they quoted $280 if they detect no damage, $750 if the detect water damage). I asked if I they can A) recover my data for me before tossing the old SSD, B) Return the old SSD with the refurbished computer, or C) let me take out the SSD before they ship it off.
They refused all 3 options. They said if I don't turn in the complete computer, including the original SSD, I will not qualify for that repair rate that the quoted me. Apparently it's a subsidized rate to replace damaged parts, so if I turned it in with parts missings I would be charged a higher full retail price for the parts and repair.
I found a solution. Despite what everyone says, there IS an SSD enclosure on the market that works with the new SSD enclosures: It's called an Apple Macbook Air.
I bought another brand new identical MBA from apple ($1500). I took the SSD out of my damaged computer and put it in the new MBA. It booted right up as if it was my old computer. I copied all the data to my network drive. I very carefully put the stock SSD back in the new computer and closed it up very very carefully, sure to not leave a single scratch or trace the computer had been opened. I put it back in the orginal packaging and returned it to the Apple Store the day after it arrived in the mail for 100% refund, no restocking fee or anything.
I felt a tiny bit bad about abusing their generous return policy like this, but at the same time I feel like they really left me no choice. They offer no enclosures for their propriety SSDs and they wouldn't even send me back the SSD from the broken machine or do a quick copy of the data from the old SSD to the new one for me... or they could even offer to test the SSD and if it work keep the same old SSD (data intact) in the new logic board, and maybe even save them some money on parts.