Earlier quoted context omitted.
For very, very popular services, a second of being live will exercise more code paths and edge cases than even the most dedicated testing team could ever dream of. We hear a hell of a lot about testing but the most fundamental piece of software quality nowadays is the release strategy: running on tee'd live production traffic, canarying, metrics and alerting, quick roll backs, etc.
That's an overly general statement. Can you do that for front-end code that stores all of its state elsewhere? Sure. Can you do it for a storage system? Absolutely freaking not. If you introduce a bug that loses or corrupts data, there's no going back. You will have committed the worst sin that somebody in that specialty can commit. Better to test as much as you can, at every level. Other kinds of code are often some…
That said, you should have tests anyway.