Firstly, hacking an iPhone to include 3rd-party apps should not be causing the iPhone to fail. Restore and thus loss of the apps, yes, but not to fail.
Not to disagree with the overall sentiment that the store people are out of line if they assume a priori that all dead phones died because they were modified, but I must take exception to the idea that hacking the phone to accept 3rd party apps could not cause the phone to fail.
Two reasons for this:
1. The mod that enables installing those apps modifies system level files, using root level privileges. This is never all that safe, but on a Mac you can just boot up from another disk & reinstall everything, so no damage done. The iPhone is not a Mac. Clobber the OS badly enough for it not to know it can't write to the restore partition & you have a big problem.
2. Apple's software is well protected against tampering, not just while at Apple but also at every step of the way from Apple to the point it resides on a user drive. (Remember kids, if you don't use OS X's Software Update app, you should do your homework & compute your SHA checksums.) You cannot say the same for the third party stuff (both OS modifier & apps) because we really don't know much about where it comes from or how good their security is.
Not to belabor the issue, but all mods are at this point a risk. If you haven't done any of them, stick to your guns & demand that your warranty be honored. If you have, you are, as Scarlet said, relying on the kindness of strangers.