How he would claim it was an official act, given that he has shown no regard for fact in his statements? Imagine the possibilities! But A74814's claim doesn't need evidence to support it: they're just quoting what SCOTUS has handed down, then noting that total immunity means immunity for all acts that can be covered under the fig leaf of "official acts". Governments do exercise the right to kill people (wars, executions, law enforcement actions) -- but not with total immunity, except under dictatorships.
Cf: Sulla, Domitian, East Germany, the Pinochet regime, Pol Pot . . .