It depends on the quality of the PSU. If you have a craptastic PSU like a Logisys, Diablotek and many others, then it doesn't matter if they're 300W, 450W or 600W, they are all likely to blow up and fry some of your other components along the way. A good quality 300W PSU should be perfectly fine, 450W is merely the board manufacturer's inflated recommendation due to the prevalence of crappy PSUs on the market.
It depends on the quality of the PSU. If you have a craptastic PSU like a Logisys, Diablotek and many others, then it doesn't matter if they're 300W, 450W or 600W, they are all likely to blow up and fry some of your other components along the way. A good quality 300W PSU should be perfectly fine, 450W is merely the board manufacturer's inflated recommendation due to the prevalence of crappy PSUs on the market.
In general, 'generic' PSUs are somewhere between bad to horrible and should be replaced with something of better quality if reliability is any sort of priority or concern.
Some generic brands like Diablotek are notorious for killing other components when they fail.