I don’t think this is true. I lived in an area where refrigerators were rare and food was too precious to throw away. Things we would consider very unsafe (like deep frying cubes of meat, and then keeping them for week) were common practice. It’s not like people were dying all over the place from it, but people did have diarrhea or nausea pretty often.
I’d say a pot of tomato sauce should be fine if it is reheated. It’s acidic, boiling will kill anything that does manage to grow, and overnight really isn’t that long of a time.
You’re 100% correct that you should use established techniques and not screw around with them, but be aware: many techniques that were passed down through generations are pretty unsafe. I’d only reccomend techniques backed by the USDA, such as those in the Ball Blue Book of Preserving or Putting Food By. There’s no magic to canning, just get these 2 books and follow them to the letter, and it’s as safe as anything you get in the grocery store. If you can follow a recipe, you can can.
ETA: You do not get used to the kind of toxins that cause food poisoning.