Why is the burden on us to disprove what they tell us they want to do and are taking actions to accomplish? When someone says they're trying to kill you and is actively working to make that happen, it is prudent to believe them.
As an aside: Iran is one of the youngest nations on earth. The government threatening is one thing. Most of the younger Iranians were sympathetic to the West. It was only a matter of time before the regime would be gone or at least soften. But when you bomb a country that generally tends to cause a rally-round-the flag effect (see Britain in WWII, for example). So we've probably blown our chance at rapprochement for quite a while. The regime can tell it's citizens "see, we warned you about America, the Great Satan! "
There is no rapprochement with people whose goal is to kill you and who don't mind so much if they die while trying.
The only way these things are alike is not useful. It's true that they both said things. But everyone understands that, even though Trump is a reckless idiot, he is saying bellicose things during a military offensive; not that he plans to annihilate Iran with nuclear weapons.
The people in charge of Iran who are acquiring nuclear weapons actually intend to use them. Besides the nuclear weapons, the quantity of conventional weapons they are stockpiling is an existential threat to Israel.
I'm going to give the Iranians credit for understanding that the intention of the US is to mitigate the threat that its autocracy poses to other countries. But it doesn't really matter. They can't be allowed to develop nuclear weapons or pose an existential threat to Israel. Neither of those aims was going to be accomplished waiting for some sort of sea change effected by an unarmed citizenry oppressed by a ruthless regime.