No. I think you're referring perhaps to executive privilege, which is something else altogether. While it is an issue to account for, saying official acts are inadmissible is far too broad.
- More precisely, not conduct but official records, even public ones like tweets, are inadmissible right? Forgive me for not looking more, I am cooking at the moment. The layman's understanding seems to be that executive privilege has been expanded.
EDIT: Having read the scoutsblog article and some of the opinions themselves, the justices seem to severely disagree over this.
The court remanded that part back to the lower courts, to determine if Trumps Tweets were in his official capacity or not. There is a good chance that whatever the lower courts decide will be appealed back to the Supreme Court again.
First, that comment references something from "the ruling" which is not part of the Court's opinion, but from the syllabus, citing pages 30-32.
> But [the Government] nevertheless contends that a jury could “consider” evidence concerning the President’s official acts “for limited and specified purposes,” and that such evidence would “be admissible to prove, for example, [Trump’s] knowledge or notice of the falsity of his election-fraud claims.” Id., at 46, 48. That proposal threatens to eviscerate the immunity we have recognized. It would permit a prosecutor to do indirectly what he cannot do directly—invite the jury to examine acts for which a President is immune from prosecution to nonetheless prove his liability on any charge. But “[t]he Constitution deals with substance, not shadows.” Cummings v. Missouri, 4 Wall. 277, 325 (1867). And the Government’s position is untenable in light of the separation of powers principles we have outlined.
> If official conduct for which the President is immune may be scrutinized to help secure his conviction, even on charges that purport to be based only on his unofficial conduct, the “intended effect” of immunity would be defeated. Fitzgerald, 457 U. S., at 756. The President’s immune conduct would be subject to examination by a jury on the basis of generally applicable criminal laws. Use of evidence about such conduct, even when an indictment alleges only unofficial conduct, would thereby heighten the prospect that the President’s official decisionmaking will be distorted. See Clinton, 520 U. S., at 694, n. 19.
> The Government asserts that these weighty concerns can be managed by the District Court through the use of “evidentiary rulings” and “jury instructions.” Brief for United States 46. But such tools are unlikely to protect adequately the President’s constitutional prerogatives. Presidential acts frequently deal with “matters likely to ‘arouse the most intense feelings.’ ” Fitzgerald, 457 U. S., at 752 (quoting Pierson, 386 U. S., at 554). Allowing prosecutors to ask or suggest that the jury probe official acts for which the President is immune would thus raise a unique risk that the jurors’ deliberations will be prejudiced by their views of the President’s policies and performance while in office.
You're right that this goes beyond executive privilege. I was mistaken. However, it still does not say official acts are inadmissible. It says official acts may be inadmissible against him if they constitute "official conduct for which the President is immune." This is an important distinction because "of course not all of the President’s official acts fall within his 'conclusive and preclusive' authority [and] [t]he reasons that justify the President’s absolute immunity from criminal prosecution for acts within the scope of his exclusive authority therefore do not extend to conduct in areas where his authority is shared with Congress."
That is to say, there are official acts the President may take that are not in his exclusive authority. Immunity in such cases is not absolute; official acts in domains where power is shared may or may not be "official conduct for which the President is immune," and, if not, they would still be admissible against him.
