Tests don't magically make changes safe or give the confidence to make changes.
At one place where I work, we're on nodejs 0.10, which is several release versions behind. It's causing us a bunch of problems, because while 0.10 is still technically not EOL'd yet, npm modules behave like it is... however we've left it so long, that the jump to current stable is a giant task, which we don't have the time for given other business reqs.
Tests indeed don't guarantee safety, but lots of small changes are easier to deal with than the occasional massive change. It's also the basic concept behind version control.
This story wasn't about trivial day-to-day developer bugs, but what kind of problems happen in really complex systems.