There are much worse things in the world than for businesses to look at every mistake as an opportunity to pick up points on the customer service front. At the very least, it keeps you from the all-too-common opposite perspective on mistakes: defensiveness.
I mean as you say, things are always going to break, whether you do shitty stuff or not. What's wrong with making an effort to make the most sincere apology you can in that case?
I do front-line support for many of our products. Partly because we're small, partly because it's important for me to get a real understanding of what users are saying.
What I have discovered is that users come in being theatrically angry. They greatly exaggerate the extent to which they are affected by problems (verified in logs), they say that they are in an emergency situation with a dying relative and need support NOW, they say they will make a bunch of bad press for the product, a few of them openly extort, death threats, etc. Maybe years of AT&T have trained them to behave badly? I'm not really sure.
Anyway, when I respond to support requests as the owner of the company, a person who has both the technical competence and business authority to actually solve the problem, not some support drone somewhere, the tone changes completely. I've actually had customers apologize to me.
So yeah, the pictures probably seem over the top, but you're probably the type of person who is polite and reasonable when they e-mail someone for support :-) Peldi has probably gotten some cranky e-mails before about downtime, and this is probably the "ward off the death threats" page.
In this particular case, I agree that the company is probably overstating their concern. And you're probably correct that this is bordering on theatrics, but the theatrics serve a higher purpose: to show that they really do care for their customers. I suspect that someone put a lot of effort into creating these theatrics. Would someone who didn't care for their customers do that? No. They'd probably use a platitude like "The customer is always right" as their slogan, and ignore their customers.
Stuff's always going to go wrong and break, it happens. Their site went down for 3 hours on a random tuesday and now this guy is throwing himself to the wolves. Come on.
There seems to be this idea that you can get away with anything, accidental or not, and so long as your rake yourself over the coals harder than the last guy everything will be okay.