Rome’s declaration of war was contingent on Carthage’s acceptance of Hannibal’s taking of Saguntum, where Carthage could have disavowed Hannibal and maintained peace. However, to even engage with this prospect, Carthage would have had to accept the terms of the offence and the interpretation presented by the Roman embassy of the treaty they held together. According to Polybius, the Carthaginian senate threw out the offence as a misinterpretation of the treaty, as well as arguing over which treaty was in place at that time.
Darius’s accession to the throne follows from a few major plot points. Firstly, that Cambyses, son of Cyrus and king of the empire, kills his brother Bardiya. Secondly, that the Magian Gaumata installs a monarch on the throne pretending to be Bardiya rebelling from Cambyses. Thirdly, that Cambyses dies. And fourthly, that the Persians retake the empire and Darius is installed as monarch.
The history of Rome is seated in surprisingly specific myth. If it weren’t for the fanciful and supernatural nature of the stories, one might even regard them as historical account. I suspect there’s some significant reality in the stories that make up the Roman establishment myth, but it’s impossible to say.