I have the most horror stories from FedEx. I avoid them like the plague. I don't think they ever delivered a "box-shaped box" to me but a handful of times. I've had to refuse a large handful of packages because the damage was bad enough.
The worst:
FedEx lost $1800 worth of computer parts that was being shipped to me. They called the day after the status changed to "out for delivery" to see if I got it (it already was a day late, spending an extra day en route. It had spent the entire day out for delivery and never showed up and I got a call after it spent the previous day out for delivery). I said "no, but thanks for saving me a call to you to find out why it wasn't delivered" and the lady was nice, but not apologetic at all. If it was a label issue that couldn't be solved they would never had the information to call me. I have bought from this place two times prior without issue.
I called the company i bought the stuff from and they sent out another package via UPS and it arrived safe, not a dent.
About a week before that tracking number went "dead" it said something about "claim processed", so I'm guessing FedEx lost it or it was stolen en route. If someone were to ship a bass by FedEx I hope they don't skimp on insurance to save a few bucks...
As I'm thinking about all this, I think I've been let down more times by poor packers than the actual carriers. How hard is it to pack an item well? It's not. It's also not expensive to do, if you've got half a brain cell. On the bottom flaps of most boxes (worth shipping in) it tells you the maximum weight and PSI load of the box. It's pretty simple math to figure out if the box will work for the item you're shipping with those numbers. It's also not that hard to give a box a quick shake to see if anything moves around, then go back and fix it so it doesn't do that anymore. It's also pretty common sense that if a box shows corner/edge damage, don't reuse it.
I think some people use/view the insurance as "I don't have to be as careful packing this now, I can make it someone else's problem".