You'd be surprised. I worked for UPS for over 6 years, lemme give you some free advice.

If it's expensive and extremely breakable - don't ship it. If you have to ship it - don't pack it yourself unless you're an expert. More than likely it will turn up broken. Ground shipping is not nice to packages.

Luckily you bought the insurance, and so long as they find that you didn't pack it like crap, they'll pay for it, and UPS is pretty good about cutting checks when they're in the wrong. Good luck, man.