For your consideration ...
Not if that person is an American on American soil, due process and all that. Hell, even Obama had American's killed when they were in foreign lands. That is not to say that "accidents" don't happen here. Most often times, (I am guessing here), without a Presidents knowledge, are conducted by the CIA or another alphabet agency.
Besides, this sort of thing DOES happen, and no one is the wiser. I still have doubts regarding Ron Brown and Vince Foster, but it's not going to matter at this point.
As I understand it - it is intended to KEEP political rivals from taking legal action against one another if during their time in office, they do something - presumably NOT killing people - that they disagree with politically. OR to simply punish themto deter others. You can't have Trump clap Biden in jail for letting 15 million illegals in and you can't have a Democratic successor put Trump in jail after his term because of some climate change legislation that he vetoed. Or starting a war. Or compelling people to take a vaccine that kills them.
Because in banana republics, that's what they do. It's no longer a difference of opinion anymore, it's right/wrong and an existential threat.
There's a presumption of reasonability that the most extreme cases are not the norm. You can't rule on a law that never has a "loophole" somewhere, but you also can't have political parties at each other's throats - at least in COURT- for executing the legitimate duties of their office.