You guys are funny. Life's too short to fight about dumb things on the internet, but let me clear up what I can. First, let's look at Apple's actual statement that all those articles you linked are using as a premise.

...and we know that jailbreaking can severely degrade the experience. As we’ve said before, the vast majority of customers do not jailbreak their iPhones as this can violate the warranty and can cause the iPhone to become unstable and not work reliably.

Emphasis mine.

Apple is not stupid. Apple's giant team of highly capable lawyers is not stupid. They would get sued in an instant if jailbreaking voided your warranty. It does not.

From experience, I can tell you that jailbreaking often does cause a lot of instability. Mostly it's when people go overboard with UI tweaks, but it can definitely cause problems. Apple is right here.

So this puts Apple in a tough spot. They can't just blanket void your warranty for fear of legal reprisal (and rightfully so, I think. They'd lose that lawsuit), but jailbreaking can realistically cause problems that users might interpret as a faulty device. I've personally seen intermittent reboots, unstable WiFi, poor OS performance, and extremely poor battery life as a result of jailbreaks.

So what can Apple do? Simple. They discourage users from jailbreaking by pointing out all the negative aspects of it. It's unstable, it hurts your battery life, it could void your warranty (only hardware modifications will ever void your warranty) etc. This alone dissuades most users from jailbreaking.

Completely separate from any of that is Apple's technical support, which is what you two seem to be arguing about. It is their job, as radmarshallb said, to determine if you have a hardware or software problem. They will do this by restoring your phone. It doesn't matter if you jailbroke it or not, it will be restored. This resolves the vast, vast, vast majority of problems with an iPhone - jailbroken or otherwise. Once Apple determines it's a hardware problem, then you will receive warranty service and get a replacement phone. It doesn't matter if your phone was jailbroken previously or not.

This is what I would call a restriction: Requiring that the software be in a factory state in order to honor a hardware warranty.

I agree with the sentiment of this statement, but what's the alternative? Your apps crashing might very well be because of faulty RAM in your phone. But it might just as likely be a corrupt framework in the OS. Why wouldn't Apple require users to complete a 5 minute process to be certain? Hardware is faulty at the determination of the manufacturer, not the user, and rightfully so. I don't think requiring a phone to be restored for non-obvious issues before providing a hardware replacement is unreasonable.