I think that there is an important distinction between 'almost-there' solutions.
Suppose that you have a piece of code that is specified to work in a certain way. Because code, and the hardware on which it runs, is made (at least indirectly) by humans, it will fail under some conditions; it only satisfies its specification. I think that we are all comfortable with this kind of "works most of the time".
By contrast, consider 'smart' products—for example, the auto-complete on your phone. This also, after a bit of training, works most of the time, and can make some brilliant inferences. However, I think that most people can agree that the "most of the time" for auto-completion is qualitatively different from the "most of the time" for specified software: it is reasonable to rely on the latter, but not, or at least not nearly as much, on the former (http://www.damnyouautocorrect.com).