A little off topic: AFAIK, initially, hot spices were invented not to preserve or flavor the food, but to hide unpleasant smell and taste of a meal's component (i.e. meat), which is a little behind its "shelf life end" being stored in hot climate. In a survival situation such a hot sauce as Tabasco may effectively hide the rotting/decomposing food smell and taste, which would warn you that something is wrong with your food otherwise.
You are are correct about the spices, but there's another factor: the organisms that cause decay are different from the organisms that cause food bourne illness (food poisoning). Those bacteria such as Clostridium botulinum, Listeria, and Salmonella emit powerful toxins that cannot be tasted or smelled. Cooking does not remove the toxins.
Fresh looking/smelling food can be deadly, and rotting food could be OK. I once consumed partially rotted ungulate bodily fluid..... "Cheddar" I think they called it.
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