Don't know the pitbull story, but got another mountain lion one...
Working in northern Montana this summer, out on a 16 mile trail run around dusk. I was yelling before corners, mainly for the sake of bears...you really don't want to surprise one. Anyway, I came around a corner and there was a mountain lion staring at me about 10 meters away. I stopped, it turned and jogged down the trail ahead. I walked for a while, yelling and shit, and then kept running, head-checking a lot, hoping I wasn't about to get pounced on.
About a half hour later, when I'm turning around, it starts pouring rain and the temp. drops about 15 degrees. I'm still shirtless and start hauling ass, trying to keep warm. Still yelling before blind corners, but sure enough, within about a mile of the first siting, I come around a corner, this time with a mountain lion running down the trail in front of me (about 20-30 meters). I assume it had heard me yelling, and was just running to get ahead and out of sight. With regular hikers this would have worked, but I was running about 5:30 pace, and kept running for about 10 seconds, completely in shock as I was closing on this mountain lion and it seemed to have no idea that I was right behind it. Finally, I yelled again, it looked over its shoulder at me disinterestedly, picked up the pace, and dropped me.