@coupland No, the reason it's about example is that it misses the actual argument.
The argument is not that a president can do whatever he wants with impunity. The argument is that a president operating legally within his legal authority can't be personally sued for his execution of the office. The suit has to be against the office, not the individual.
So presidents can't assassinate political rivals with impunity because that wouldn't be a legal part of carrying out the office. The example just doesn't apply.