Can I reasonably request a refund from the airline on the grounds that that should not be possible?
Maybe, but that depends on the airline.
Most airlines booking engines will not allow you to book the same ticket twice. It's explicitly not allowed in their terms and condition. On some airlines you CAN buy an extra seat (for extra space) for yourself but that needs to be booked through a different process.
they expected two passengers with my name
That sounds like a lame excuse. Same name for two different passengers can happen, but same name and same address, credit card, or airline account being different persons does not. So maybe they screwed up here themselves which may make the more inclined to negotiate.
I recommend checking the airlines terms and conditions on double booking. You probably can find some wording in there that can help with your negotiation. "your terms and conditions explicitly disallow double bookings, why did you accept mine?"
At the end though, you are at their mercy: you bought two tickets and the airline sold you two tickets. It's not their fault that you only wanted one.