Truman thought he had authority, and so criminal immunity was not required for Truman's decision to seize the steel mills. There was no criminal intent. There are often different interpretations of laws. Acting under a mistaken good-faith interpretation of the law is not a crime for government officials.

No doubt. But proving that element of mens rea is a defense to a charge of a crime - not a basis for immunity from prosecution. IOW, even though Truman (or Obama) would likely prevail in a criminal prosecution by presenting evidence that his actions were founded on a good-faith interpretation of the law and not simply a callous disregard for someone else's property ownership, that's a factual question to be determined in the course of the prosecution. It's not a slam dunk, in Truman's case - lots of people were very vigorously arguing that he was breaking the law in taking that action. Proving that he didn't believe them, that despite there being objective arguments for why his actions were illegal that he didn't act with that state of mind, is a defense to be asserted in the prosecution. Not immunity....

...unless you adopt a rule that says that Presidents are immune from prosecution when they are acting within the scope of their authority, even where there is a strong claim that their actions were unlawful.

We've never had to parse that out before, because prosecutors have never gone after a former President for actions they took while President. But I don't think it would be too difficult to find a "conspiracy to defraud" charge against every modern President, because every modern President tries to hinder Congress from doing something. I mean, that's part of the point of checks and balances - Congress and the President are somewhat in competition in trying to wield Federal power, and there's always something that the opposition Congress is trying to do that the President would like to slow/stop (and vice versa). Is the President subject to prosecution for interfering with official proceedings every time he tries to thwart a Congressional committee from doing something he objects to? If not, what's the rule that we apply to reach that conclusion? 'Cause I bet it's going to look a lot like immunity....