You're taking "cutting corners" out of context. He is describing how individual nodes don't need to run at the standards of regular data servers and are hence cheaper, but in aggregate provide a reliable service.
Not really. Just probability.
If you have fully redundant services then ALL of them have to go down to have an outage.
Suppose you 5 copies with 75% uptime each.
The probability that all of them are down is 0.25^5 ~ 0.0009
Now of course that assumes they are uncorrelated, but since Sia nodes are distributed across the internet, that's likely as opposed to multiple servers at a few data centers like AWS.