Wut.
That's because things are built with certain tolerances. For example, engine components are specifically engineered to be able to withstand a certain amount of stress for so long, but that doesn't mean that they can't be stressed further, just that they aren't guaranteed any further. That has nothing to do with being "more than the sum of its parts" at all. Nor does it have anything to do with this topic. That phrase insinuates a certain emotional element that we humans apply to machines. The machine will be able to perform up to when it fails no matter what we feel or think about it.
Many people for a very, very long time have experienced otherwise, whether it's because a human projects unto a device or perceives through a veil of emotion is functionally irrelevant.
Don't take my word for it though, look into it. Aircraft are a good dramatic example since when they fail, you generally die. Talk to some old pilots, check out the author I mentioned. That saying "there are no atheists in foxholes" applies, when you're high in the air and the possibility of being on the ground in dramatic fashion presents itself, you will speak to your aircraft and it will be more than just a machine since it's the only thing preventing you from ceasing to be.