It's my understanding that for bacteria to grow when meat is being thawed, the bacteria has to be on/in the meat to start with?? Yes, it can mulitply, but the the bacteria was already in the meat.
As long as you cook the meat throughly, to the correct temperature, you are fine. If you undercook it, even if it was fresh or thawed in the fridge, you could be in for some trouble.
It's kind of like the salmonella/chicken egg thing. some obscure number, like one in 2 million eggs, has the salmonella bacteria. Over 90% of those infected eggs come from New Jersey. What are the odds that I'm going to get sick from my cookie batter out here in Washington eating locally grown eggs?? Are you kidding - salmonella vs chocolate chip cookie batter ?? You might as well put Johnny Fairplay in the ring with Wladimir Klitschko
Totally worth the risk in my house.