Perhaps the immortality part was an exaggeration, but I was thinking about the way the Kremlin avoids admitting any health problems of the leaders. That happened in case of Yeltsin and allegedly in case of Putin's absence in March this year. Recently there was an interesting article about this "health PR" dating the tradition back to the USSR era, but I can't find it right now.
This is hardly unique to Russia - after all, FDR avoided being photographed from the waist down and wore special braces when standing and Kennedy had many secret health problems. I think this is more a fact of projecting an image of power in any society.