Viktor Mikhaylovich Sukhodrevwas a Soviet Russian personal interpreter for among others, Nikita Khrushchev and Leonid Brezhnev, Mikhail Gorbachev and Alexey Kosygin... (wikipedia)
You always have to remember your place. You can be close to the person, but you must know who you are and who he is. It's a fine balance. A delicate balance. It depends on your upbringing.
You cannot stop to ponder. You just can't. If you do, you fail. You simply stop.
An interpreter at that level cannot - not 'should not' - simply cannot, make a mistake. He cannot. No way. Well, if he did he'd be out, and rightly so.
It's an almost mystical feeling that you are bringing people together, people who otherwise would never be able to communicate.