There are two quite different sorts of problem with salmonella. Some salmonella, like typhimurium, will produce acute food poisoning symptoms almost immediately. I think this is similar to staphylococcal food poisoning, which is due to a toxin produced by the bacteria while the food is sitting rotting in a shop or your larder. It is not due to live bacteria in your gut. Cooking tends to destroy toxins but gentle cooking like scrambling eggs will not.
The second problem comes with salmonella that are pathogenic because they breed in the gut itself. Typhoid and paratyphoid are examples which produce bleeding. I think there are other forms that produce something more like dysentery with diarrhoea. These take a few days to show problems.
My guess is that eggs that had gone off enough to form toxins would smell nasty, although I am not sure about that - so maybe a toxin problem is unlikely to come from the eggs - maybe smoother ingredient?
I agree there are different toxin effects from different microbes. Just to add a bit:
Staph aureus produce exotoxins externally to the cell so you don't need to digest the cell for it to be released. However for this to be a problem you have to have a lot of staph on the food before ingestion which means that human skin has to be in contact first to contaminate the food either as a gross contamination or more likely it has to grow for hours or days before ingestion. To grow on the food it needs to have had poor temperature control after preparation and time to grow.
Staph is unlikely to have been in the egg to start, only when it's been prepared. You can't tell toxins by taste, but the abuse of the time/temperature/loading will cause other microbes to grow as well, potentially giving you an off smell or taste. In this case the eggs would have had to be prepared by someone with staph on their skin that hadn't washed their hands/ worn gloves etc left on the counter for a few hours on a hot day etc before ingestion .... so very unlikely in a home environment for scrambled eggs.
Salmonella sp will cause food poisoning rapidly (less than 12 hrs) only when the food or water ingested is already very heavily contaminated. This is mainly from direct human faecal contamination as with typhoid. As you say in this case the egg wouldn't have been in contact with enough faeces to have had such a high loading.
All Salmonella species/types produce an endotoxin and is infectious in humans (grows in the gut). The toxin is different to staph in that it is contained in the cell and is only released once digested. So you can get infected by lower levels of cells from food, but there is a delay in symptoms 24-78 hrs (typically 48hrs) to allow the cells to grow and release their toxins Into the gut and give the gi symptoms. The cells can also enter the bloodstream through the gut wall in some cases. Infections of this sort come about mainly from eating contaminated food that has not been cooked fully. But you would still need to wait for longer to see effects. Symptoms would include fever violent vomiting and loose stools enough to cause severe dehydration that would need hospitalisation.
In short you have to try very hard to get food poisoning and this needs a combination of high contamination, poor storage, poor heat treatment during and after cooking to cause a problem.
Symptoms are often far more severe in terms of the violence and duration of reaction than most people think.
Salmonella is rapidly destroyed by heat so if anyone is worried, buy a temperature probe and cook all chicken and eggs to 72deg C or higher and buy food from large manufacturers who have more to lose by not following the correct food hygiene standards.