I'd say it's mostly busywork and the placebo effect of thinking it took less time to type a Vim text-editing command than do it in another editor.
And that's for a marginal use case programmers don't fall much into (if you're frequently re-arranging lines or performing the same actions of blocks of text, then you aren't exactly programming).
I'd believe this if it was coming from a vim programmer, but generally speaking this claim does not come from someone who uses vim so doesn't carry much weight. Are you highly proficient at vim and still believe it is a placebo effect?
Even a small improvement in iteration time has a dramatic effect in the way you approach problems. Vim lightens the mental overhead on making text manipulations so that you simply think about what you want to do and your fingers do it.
And that's for a marginal use case programmers don't fall much into (if you're frequently re-arranging lines or performing the same actions of blocks of text, then you aren't exactly programming).