An old say that "you can't run out of fuel if you don't burn off the bottom half" means that if one doesn't burn the tank below 1/2 tank, one doesn't run out of fuel.
Unfortunately, there exists more than one way to run out of fuel. Exhaustion, running completely out of available, fuel, is one way. Fuel starvation is another...often leading to exhuastion. Fuel mismanagement still continues to be a significant factor in aircraft mishaps.
The phrase itself, regarding burning from the bottom half, is sometimes taken literally by those who complain that they'd never get anywhere if they always stopped burning fuel when arriving at 1/2 tanks. While apparently the intent of the saying has eluded such individuals, the intent that one should keep a healthy reserve is still valid today. No regulation nor law exists which suggests that one must always rely strictly upon minimum fuels as one's personal minimum.
While we found a 4% penalty in the 747 for extra fuel carried (4-5 percent of tankered fuel is burned just to carry the fuel), we also often found that the penalty was worth the cost for the safety margin, and carried the fuel.