True.
The same is said of AIDS. People don't die of AIDS, they die because their immune system is so compromised that the flu kills them or something else.
I agree that there are things that kill you easier when you are older than when younger, but there are a lot of things totally unrelated to age that are already killing us, things like an unhealthy lifestyle leading to obesity and diabetes. You'll probably agree that there are very few fat old people (like _really_ old).
While there's a lower risk of heart disease in younger people, this might likely be because they just haven't had enough time to do the full amount of damage required to finally cause it to fail.
So we should see (purely for the sake of argument) what causes of death are due to an otherwise healthy body being old, and what causes of death are due to an accumulation of time doing something that may kill you.