The problem with cooking food and then allowing it to cool in the correct manner is that although it kills off the food poisoning bacteria that are in the normal (vegetative) state ie, the ones that are growing and multiplying, there are a small number of bacteria that have developed a defence mechanism.
The are bacteria such as Bacillus Cereus and Clostridium Perfringens, to name the main ones, and what they do is to form a protective casing around their nucleus.
This occurs when conditions are unfavourable, such as during cooking, but can also be due to high acidity or some others.
Normal cooking temperature is not usually able to kill off those spores, which remain dormant until more favourable conditions arise.
These can be killed by rather higher temperatures, but we will leave that for the moment.
So, you cook your food, preferably above 75C although 70C will likely be ok, and chill it rapidly to below 4C.
This means that the few remaining bacteria in the form of spores do not get much chance to regroup, its now too cool for them to multiply.
You can eat this cold, within a certain period of time.
Your next option is to heat it up, but if you only heat it up to , say, moderately warm such as maybe 30C-40C, those spores will have ideal conditions for multiplication, and this can be made very much worse by holding this food at such a temperature for a period of time such as on a hot trolley, or counter display.
The manufacturers will usually state that you can only safely reheat food once, and by ‘piping hot’ they actually mean back up to cooking temperature 70C-75C.
Rice is one notorious risk in this category of food, as it harbours Bacillus Cereus, and rice is often pre-prepared for later reheating in fast food places such as Chinese and Asian restaurants.
Storage of pre-cooked foods must always be done at either hot temperatures, above 63C, or below 4C, and never anything in between.
If you want to reheat the food, the advice is only do this once, and always to cooking temperatures 70C-75C and always all the way through - localised cooler areas may allow bugs to multiply.
If you are already keeing cooked food at 4C and you reheat and consume absolutely immediately, like you might at home, then the spores will not have enough time to multiply to an infective level, however the food suppliers cannot know what you intend to do and so make the safest recommendation by assuming people will hold food for periods of time before consuming.