Yeah. He's talking about how we ALL know the SETI software that uses your processor when you aren't. I hear NASA wants in on this idea to boost thier computer power.
To your processor? I doubt it. Sounds like you install a program which lets the processor connect to the grid. Anyone signed in can use a piece of your CPU, if it's not busy. Hard drive and memory access should still be controlled by your O/S, if your drives aren't shared or they have share passwords, no one else should be able to get into them. But it could happen, it already happens online. And the way Windows tosses around chunks of memory, I wouldn't recommend plotting anything too evil or too good on a system which is in any way connected to the outside world. But since I don't do much plotting, everything I think of has already been thought of before, I might give this a try. Who knows, someone may be able to factor that 512 bit number into the 2 prime numbers they need