Yes, the key here is this, in the immunity E is talking about the elected official or police officer would not have a say in if what they did was an official act...but a POTUS does have a say in whether whatever they do is an official act. 

Trump, and the 6 members of the Supreme Court have backed him, believes that anything he does while president, anything including harassing a woman he sexually assaulted, is an official act. He can stand by that statement because he believes as president he is the country, he is what is good for the country, and so anything he does for himself is for the good of the country as well. Hence, the president can make the call if something he is doing is a crime or not.

It's totally absurd but the Supreme Court just said, nope, that is what we believe. So, all a president has to say is "I believe I was acting in my official capacity." and now the court, any court, is supposed to take that as reason not to prosecute him.

Watch what is about to happen in the two Jack Smith cases now that they have made this ruling.