Hi! I'm a real big dumb dumb, cause I never, ya know, studied law. But I sure do know that with SCOTUS decisions, the dissenting should be read as well, to get the proper context of the decision that the opinion won't state. Sotomayor sums up the majority decision like this, and she's a damn sight more knowledgeable than I could ever be:
The majority makes three moves that, in effect, completely insulate Presidents from criminal liability. First,
the majority creates absolute immunity for the President’s
exercise of “core constitutional powers.” Ante, at 6. This
holding is unnecessary on the facts of the indictment, and
the majority’s attempt to apply it to the facts expands the
concept of core powers beyond any recognizable bounds. In
any event, it is quickly eclipsed by the second move, which
is to create expansive immunity for all “official act[s].”
Ante, at 14. Whether described as presumptive or absolute,
under the majority’s rule, a President’s use of any official
power for any purpose, even the most corrupt, is immune
from prosecution. That is just as bad as it sounds, and it is
baseless. Finally, the majority declares that evidence con-
cerning acts for which the President is immune can play no
role in any criminal prosecution against him. See ante, at
30–32. That holding, which will prevent the Government
from using a President’s official acts to prove knowledge or
intent in prosecuting private offenses, is nonsensical.
You should really read it, it's such an important read.
PS: Sorry for formatting, it's copied verbatim from the dissenting pdf