I've never looked too much into power supplies but wouldn't a failing supply deliver dirty electricity thoughout the system leading to possible hardware failure and/or disk corruption?
Not if it can't deliver power at all. All of the failed power supplies that I've seen (at least in this nature -- smoke, fire, sparks, etc) are bad because of a short circuit. Power never leaves the PSU.
I'm sure other forms of malfunctioning PSU's do that sort of thing, but none that behave in the way Newby described.