Organisms' mutation rate is not constant: there's a need to mutate more due to the need to be able to adapt over generations to novel threats, and a need to mutate less due to the risk of premature (before reproduction) death. This adaptability also explains why whales, which are much bigger than us, don't all get cancer almost immediately and die young; and also why dogs, which are much smaller, still often manage to get it despite only living to 12 or so.

In computers… well, there's multiple layers of error correction. There's error correction in the link layer, in the transport layer with TCP, at the OSI application layer implicitly in TLS because errors would break the signing, and important files also get separate checksums (and these days security signatures) to be tested when the transfer is complete. These were all designed with arbitrary standards of "acceptable" error rates, there's nothing to prevent a new design with a different idea of what's "acceptable" and setting that threshold as low as I suggested, or even lower.

But!

Every time I see someone make a pronouncement that they're more than 99% confident of something they've never actually tested, I think they've likely not thought of all the ways their thing can go wrong. That means that while I can be confident that we can design a system that appears, according to every scenario we can imagine, to have less than a one-in-a-trillion chance of a mutation surviving even if every atom of the universe is converted into more von Neumann probes implementing that system, even then I still expect that if it were built it would rapidly encounter an outside context problem.