Well done meat can counter a number of contamination issues, but can't undo toxins already created by bacteria in meat that wasn't kept to a safe temp or a lot of really dangerous stuff like mad cow disease.
Yeah, toxins are often the bigger risk when dealing with bacterial or fungal issues.
For instance, botulism is caused by the toxin produced by botulinum bacteria. The toxin is a paralytic. The bacteria itself can typically be dealt with by the immune system, but the toxin wreaks havoc on the nervous system.
That’s also why you should never feed honey to babies; botulinum is commonly found in honey. Babies’ immune systems aren’t equipped to deal with the botulinum bacteria, which allows it to bloom and start producing the toxin after they ingest it. This causes something called Floppy Baby Syndrome, from the baby being paralyzed by botulism toxin.
It depends on the bacteria, but in short the toxins are bacteria waste and it builds up the more active the bacteria are and how many there are. That is also why you can't just reheat already cooked food to make it safe again.