The prosecution must prove mens rea. Truman had none, and so the prosecution fails.

The prosecution might indeed fail. People are acquitted all the time. There are also people who are arrested, arraigned, charged, and go through the early stages of a criminal prosecution before getting their cases dismissed on a legal point.

But that's not immunity. Immunity is that you can't be charged in the first place - you're immune from prosecution.

Plus....are you sure you can't prove mens rea for Truman? Despite his protestations, it's not like the outcome of Youngstown was a complete and total shock - there were plenty of well-founded legal objections to what Truman did, the action was widely excoriated in the press, and the Administration lost at both the trial court and the SCOTUS level. Mens rea is tricky - it's almost always proven by circumstantial evidence, and there's plenty of evidence that Truman knew that what he was doing was unlawful (certainly plenty of people telling him it was).

I mean, I agree - probably not enough to convince a jury. But you could probably convince a judge that there is enough evidence to ask the jury to rule on whether Truman knew (or should have known) his actions were illegal. Same thing with the Obama case: certainly the President will claim that he felt that he was within his rights to refuse to cooperate with the Congressional investigation, and that's probably where a jury would land - but it wouldn't be hard to assemble some evidence that he knew (or should have known) that his position was wrong, and that the prosecution should be allowed to put it to the jury.

Again, there's a difference between "the prosecution will probably lose" and "the President is immune from the suit."