"It's possible (and not that hard) to define an integration process that prevents faulty commits from being integrated to the main branch. "

You should strive to do that but you shouldn't be surprised that despite all effort mistakes still happen from time to time.

Sure, mistakes happen, which is why the process is typically automated. You have to go out of your way to merge faulty code. It's rare.

Not saying mistakes can't happen, but the person I was replying to didn't seem to be aware of this tooling.

You're both right.

The healthy mentality is to realize mistakes will happen. This creates a healthier culture when things do break.

However, you should take every step to ensure it doesn't happen. You should act as though you want to prevent all faults from hitting you master branch.

It depends on what you means by “errors on master”. Tests won’t catch all possible bugs in production.