In this case, I think the assumption that doesn't bear out is "stable amount of population". The relationship between death rate and expected lifespan is likely calculable, but only if you also have either age data or at least approximate change in birthrate data, preferably going back to living memory. We might have that available somewhere, but I don't think your estimate came from having it.

Like let's say there's a terrible war, and half of all people die. Can we conclude that most people are dying around 2? This example is extreme, but shows that we at least need some averages over time to start making a case for life expectancy being predicted well by the data