It's related to the quality of the components used to build the power supply. Generic ones are usually very low quality and can die in less than 1 year and kill one or more of the components attached to it (such as your graphics card, motherboard, or the entire system).
Getting a recommended power supply means that the chances of this are so small that we can say that you're practically guaranteed that it won't happen. But with a generic power supply, you are putting your system at risk. Generic PSUs are usually best reserved for low-end office computers that never have to do anything strenuous.
Worse yet, doing any overclocking with a generic PSU has a history of guaranteeing the eventual death of the PSU and one or more components (sometimes the entire system again).
In other words: the PSU is the single-most important component in the entire system because everything absolutely depends on the PSU! If we humans could buy ourselves a new heart, then which would you rather choose: a generic heart, or a quality heart even though it costs much more?