If a population has always contained 1,000 individuals and, over a thousand-year period there have been 500,000 births and 500,000 deaths, then (ignoring phasing effects) the average lifespan of the population will be two years. Even if 999 individuals live 1,000 years and the other 499,001 individuals live for 63 seconds each, the average lifespan would still be two years.
Likewise with lifetime birth rates. If there are 1,000 individuals and, over the course of a decade, one of them has 5,000 offspring and the others have zero, the average birth rate would be five per decade.
These averages are completely unaffected by distributions. It may well be that they do not represent typical members of the species, but numerically they are what they are.
Typically in a wild population death rate is a function of age. I can't post a plot, but consider death rate per age group vs. age. I'll use a step function for simplicity. The death rate for 0-2y/os is 0.4. The death rate for 18-20y/os is also 0.4. The death rate for 2 year periods in between is 0.025. The average lifespan is 10 years, but the death rate over those ten years is 0.5, the same as the birthrate in this thread.
In such situations as hard winters, drought, predators and hunting the death rate is also proportional to the number of animals present and the magnitude of the adverse situation. As the number of animals goes up, the death rate increases.
These complicaitons were simply left out of the problem. They are implied by the givens. There's no reason to claim contradiction.