Only chink in that theory is rapamycin doesn't seem to have anti-aging effects per-se, rather a wide array of systemic effects, some beneficial to longevity in special circumstances. In the general case, you definitely won't be extending lifespan of the elderly by modulating down their immune system or promoting amyloid formations.
There is definitely "real" randomness, DNA replication errors are truly random because they are caused by quantum molecular effects. You can characterize them statistically and reduce their incidence, for example by controlling the diet or shielding the body from UV, but you can't measure those causes, only observe their effects. At best you could correct them, starting from a known-good-copy, as indeed cell biology already does.
There is definitely "real" randomness, DNA replication errors are truly random because they are caused by quantum molecular effects. You can characterize them statistically and reduce their incidence, for example by controlling the diet or shielding the body from UV, but you can't measure those causes, only observe their effects. At best you could correct them, starting from a known-good-copy, as indeed cell biology already does.