The charts are only a starting reference point. The water in the meat will Pasteurize at temperatures between 131 degrees to 167 degrees for at least 30 minutes. So with low slow cooking you must error on the safe side and get above 167 degrees and hold it there till the cooking is complete. Since bacteria cannot penetrate very deep in a solid piece of meat, all you have to really Pasteurize is the outside surface. So things do not have to be that hot inside to get the meat safe to eat. Hamburger is the exception. It can have bacteria internally because it is all mixed up in the grinding process. hamburger should always be cooked to above 167 degrees through and through and even hotter if the cooking time is shorter than 30 minutes.
The real variable in cooking meat is how much connective tissue or collagen must be broken down in the cooking process. But here is the conundrum. If you heat the collagen to a temperature greater than 280 degrees you will set it and then no amount of cooking will break it down. Also beef comes in two types. The first type is support muscles, and consists of muscles that only hold the animal together and up on its legs. This type contains very little collagen because it does not need tensile strength. Therefore you can cook it up to temperatures as high as 500 degrees without making it tough. Rib-eye, prime rib, and fillet minion are all support muscles and can be cooked high and fast without becoming tough. High and fast cooking will also boil off less moisture than low and slow cooking so it produces juicy meat naturally. The other type of muscle is locomotive muscles that make the animal move. It needs high tensile strength and therefore contains a lot of collagen. You need to keep the temperature lower than 280 degrees when you cook muscles of locomotion. Round steak and brisket are both locomotion muscles and must be cooked low and slow if they are to become tender. You must also watch the low and slow cooking because it applies heat for a long time and moisture can boil off and make the meat dry. Therefore we use tricks like foiling with water added to prevent this. You can also cook support muscles low and slow but it is not necessary for tender meat and can dry things out too much. Poultry meat is all low collagen and can be treated like beef support muscle. Pork has less collagen than beef so it is less likely to be tough, but the rules still apply. With pork I find that the problem is drying out more than getting tough, because you cannot serve pork rare like beef.
So temperature is important and if you do not understand the needs of the meat you are cooking then you cannot do more than follow somebody else's formula to the letter for a successful cook off. If you ever try to experiment without the above knowledge you will more likely than not get bad results, and to me the experimenting is what makes cooking fun.