I think people thought they were outsourcing the job of not having a single point of failure.
Having a critical service supplied by someone does not necessarily mean there's a single point of failure, because that someone might be working to make sure there is no single point of failure.
But, outsourced or not, critical things should be as redundant as needed, and not relying on a single point of failure.
If in a hospital a life-keeping machine depends on electricity, I hope they have diesel generators available even if their outsourced power supply fails.