The big issue is, what does this style of interviewing do for you with a real-world candidate selection challenge --- say, 3 developers, all similar on paper?
There is no reason the best candidate necessarily has the best story. The story of your "best accomplishment" has as much to do with random chance as it does with capability. This question demands that an interview somehow de-confound the luck element and the skill element.
And to what end? Even if you got a clean reading on this question, somehow equalized between the candidates, I ask again: do you really know a lot more about how the candidate will actually perform on the job? Because that is almost the only question that matters in candidate selection.
"Gee whiz, I'd say my biggest flaw is that I'm TOO passionate about technology!"
Maybe I coded an iphone app. Meanwhile you coded an iphone app, and fixed bugs in a huge legacy codebase, and did hiring and code reviews and mentored new employees, and contributed to open source projects, and introduced your company to source control and automated testing, and masterminded a trivial code change that made the company a million dollars a year, and you spend your free time running a programming club at a local orphanage.
If we're competing for a job and we're asked about our single biggest achievement, we'll both say iphone app. An employer who wants to accurately gauge who is the better employee should probably dig deeper.
Say I saved a million dollars a year by adjusting a configuration setting, no coding required. That might go over well with a business type, but if the interviewer is all about the programming, it doesn't demonstrate technical mastery. There will be no scope for talking about the technical challenges, the languages and databases I used, what I learned from the experience, or how much I enjoyed it and grew as a person and a professional.
Say I introduced source control and automated testing at a medium sized company. Again, the technical work is limited - you can install Jenkins with apt-get, the real challenges are political and educational, changing 'official' workflows and 'supported' software and convincing people to sink time into using the tools for long enough that they can see the benefits which are not immediately apparent. If I'm being interviewed by a young guy at a startup they might think they have no politics so my skills will be useless - or worse that I'll introduce politics. Or it just won't seem like much of an achievement, after all the six of us at this startup switched from bzr to git in an afternoon.
Needless to say, if the original job description says "wanted: someone to teach us source control and automated testing" that would be a different matter :)
whereas others cap at, "well, I did manage to build the world's first and largest bitcoin currency exchange and reach volumes of about a million a day before we had to shut down."
when you find out they did it by themselves, that is a huge difference. like two orders of magnitude FTE's.
it's like, if some guy spearheaded and came up with the whole idea behind the new Mac Pro, in an era of stagnant desktops, the whole mechanics and central idea (with the heat core). This question lets you know this.
a million examples, this is really just one.