There was a This American Life episode a little while back that had a counter example to this anecdote: sometimes there is something in your process that makes your product special but you don't even know it until it disappears.
Audio here[1] at 34:30. A brief summary found here[2]:
"Jim Bodman, Chairman of Vienna Sausage Co. in Chicago tells the story of how the company built a brand new, state-of-the-art facility in 1970, replacing their old factory, which was actually a warren of buildings on Chicago's south side that was built up by gradually buying up buildings over the course of 70 years, until the factory complex occupied an entire city block. Once they moved into their fancy new digs, however, they faced a problem: the hot dogs weren't coming out the same. They didn't have the same distinctive red color or desired snap. They couldn't figure out what was wrong, since the ingredients, spices, cooking time, everything was the same.
After a year and a half, they still haven't figured it out...until one night, when some guys from the plant are out at a bar, reminiscing over drinks about the old days in the former plant. They start talking about Irving, a fixture at the old plant who knew everyone, whose job was to take the uncooked sausages to the smokehouse. But, given the "Rube Goldberg" layout of the old factory, it took Irving half an hour on a circuitous route to get from A to B. And they realized: Irving & his trip was the missing secret ingredient."
[1] http://www.thisamericanlife.org/radio-archives/episode/241/2... (audio at 34:30)
[2] http://theatreeastnyc.blogspot.com/2011/10/how-sausage-er-th...