If I were a non-empathic person who'd chosen a strategy of following the rules to blend into society, I would find it very inconvenient for people to think I was anything like him, and would therefore attempt to emulate empathy under most conditions.

That's exactly how I approach the situation. I find the claim that I can't be moral without empathy just as ridiculous as you would find the claim that you can't be moral without believing in god. I also find moral philosophies that depend on either of them reprehensible. Claiming moral superiority because of thoughs or affects that are easy to feign is just utter status grabbing in my book.