With web, at small scale (which honestly is 95% of the world), you just version and back up everything. We push updates that break stuff from time to time. If it's bad enough, we just hit a button and roll back the change. The nerves are basically a sign that you need to have an easy rollback process in place, once you have it, you sleep easy and things are fun.
Clearly that's how they ended up with the current team. They hired for culture fit. Anyone who worries too much is out.
You bet they have an amazing perfect top-notch hiring pipeline, many rounds of interviews, and whatever you could wish for! (No, no ... the subcontractors writing code are not in scope for this, duh.)