Strength and conditioning is VERY important for a fighter like Amir. It's no coincidence that his best performances (Judah, Kotelnik and Paulie) came off the back of sound S&C camps with Alex Ariza, and his worst performances (McCloskey and Peterson) came off of camps that either lacked S&C altogether or were with someone else. Ruben Tabares isn't S&C qualified to the degree of Ariza. Manny Pacquiao has neglected S&C for Marquez 3, Bradley and Marquez 4. Look at the results. S&C is essential for fighters that rely on their physical attributes in the modern game imo.
S&C is very important, but it is not the reason for Khan's uncanny ability to get himself knocked on his fanny... that my friends is due to his insistence on fighting like a dick, nothing more.