160 isn't a magical temperature. It's the temperature where many bacteria that cause food borne illnesses become unable to reproduce and start to die. It destroys their cell membranes. That temperature doesn't kill all bacteria, and it doesn't render any food 100% safe. What it is very effective at doing is eliminating most of the common types of the common kinds of bacteria such as Shigella, e. coli, salmonella, and clostridium perfrigens. But it does not kill all kinds. There is a strain of e. coli, for example, that is both thermally tolerant and lethal to humans. But it is very rare. Perhaps most importantly, bacterial infection isn't the only risk at hand from consuming food that has bacteria on it whilst it was cold. Most bacteria produce toxins as they multiply and die, and heat does not deactivate them. This is how botulism kills people, but many common illnesses are caused by toxins as well (like Shigella and bacillus cereus aka "fried rice syndrome"). Bacteria produce these toxins readily between 40 and 140 degrees F; between 140 and 160 they stop reproducing (much like the <40 area, save for the important exception of Listeria) and above 160 they start to die.
However, there are certain illnesses that are not preventable by cooking at all. I've already mentioned toxins produced by bacteria, but there are others: protozoan sources like cryptosporidium parvum (which comes from human feces infecting the water supply of the food you're eating), is unremovable, and fish can carry Ciguatera toxin and scombroid, which causes histamine poisoning.