Much of this is untrue. Many snakes, even pythons, will opportunistically eat dead animals such as road kill, and often in a state of putrefaction, without harm. Snakes MUST deal with food that is quite quickly not "fresh" - a snake which eats a large prey item, even a Carpet which eats a fair sized rat, will have to deal with the rotten contents of the gut of the rat when its stomach juices eventually penetrate the gut cavity, which can take days in some instances. Snakes don't do as mammals do - chew their food and mix it with saliva bfore swallowing it and sending it down into a bath of hydrochloric acid, which, incidentally in mammals, is further quickly mixed by the muscular activity of the stomach.
Anything larger than a half-grown mouse or rat is going to mean the snake has to deal with putrefaction as part of the digestive process, and as long as temps (the most critical factor at this time) remain suitable, there will be no problem, because it's routine. That's why you should NEVER feed snakes large meals when anticipating a heat-wave or a cold snap - when it's very hot, the food will decay faster than the snake's system can deal with it, and in cold weather, the snake's system will once again be too slow.
To suggest that snakes will suffer if given food that's a bit "off" is like saying your dog will die if it digs up and eats a bone it buried 2 weeks ago - of course it won't - neither dogs nor snakes have anywhere near the sensitivity to "germs" that we humans do.
Having said that, naturally we like to give our snakes (& our dogs) fresh food. But on the odd occasion that a rodent or other food item has been rejected, and it has been previously quickly thawed, it is certainly OK to refreeze after a couple of hours, to try again later.
Jamie