A lot of vinegar based sauces have shelf life past their expiration just sitting in a cupboard. However, sauces that have more fruits/general chunks of junks should definitely live in the fridge and be carefully monitored for mold.

Also, almost all condiments you use at restaurants (ketchup, mustard, hot sauce) are not stored in the cooler overnight. BUT! The turn-around for new condiment bottles is fairly quick.

I store ketchup in the fridge out of parental habit.