Sick Dog? Sometimes All You Have to Do is Patiently Wait

I want to be clear - Do you mean waiting once you've visited a vet and are sure it's something like a simple upset stomach? Or at the first signs of illness?
I think the waiting should happen after an a initial vet check-up if the vet says this is the route to go... I know vet visits are horribly expensive but if there's something wrong, it's worth it a million times over. The "just wait it out" thing can be dangerous to tell other dog owners who might not know how to recognize certain signs and might mistake serious internal issues for an upset stomach or gas, for instance.

I know my story isn't typical, but a few months ago my dog, Apollo, started acting strangely. He was lethargic, shaking more than usual, wincing when I pet him, and not eating. On the second day of this, I told my husband and grandmother that I was sure something was seriously wrong. They told me "just wait it out". The next day his gums had gotten pale and his ears were yellow-ish. They still told me I was worrying too much and seeing things just because I was just looking for something to be wrong. They were sure it was just an upset stomach that needed time to pass and told me that it would be silly to do anything but patiently wait... I took him to a vet. The first vet also told me "just wait it out" after taking care of his fever. I took him to another vet. His temperature was so high that the vet was shocked he wasn't passing out. Blood test results came in the next day: The enzyme levels in his liver and pancreas were so high that the vet wasn't sure a recovery was possible at all. He gave me a few treatment options telling me that they're not likely to work... luckily they did, the happiest day of my life was when I found out. However, if I had just waited it out like countless people told me to do - even a single day longer - it would be hopeless...
I fear that other dog owners may not know to do things like look at the color of their ears, gums, and whites of their eyes. Even if they do, this doesn't tell the entire story. But even constipation and an upset stomach can be helped. Waiting is part of it once a trusted vet has confirmed what's wrong, but it's the last step to take.