There had to be something way wrong with that cat, I would think the noise of the chain saw alone would be enough to keep it away.
We see cougars every now and then when were deer hunting, they are spooky critters. You see em then there gone, then you see see em again latter and understand it's following you at a distance. Makes the hunter feel like the hunted real fast. I've never had an issue with the ones I've seen but they do make you feel uneasy even with a hunting rifle in hand and a pistol on the hip.