Whether it's FEDEX or UPS, the condition a ball arrives in has much to do with how the local office treats packages. My UPS is pretty good, and FEDEX has gotten a lot better.
Previously some FEDEX bowling ball boxes looked a lot like yours: as if someone tried to bowl with the box in a parking lot. The box got beaten up very badly and the appearance went from a cube to a being rounded at all 8 corners. Thankfully, most people double box and the the two boxes protected all balls from external damage.
Just because you insure the package (or get $100 free insurance) does not mean they pay for the damages an internal item receives. I learned that the hard way when a CD player was grossly mistreated and dented. The buyer refused to accept the package. UPS, AFTERWARDS told me that their web site specifically says that electronic items MUST have a 3" buffer of packing material like foam in all 3 dimensions between the item and the cardboard outer box. I only had 2".Luckily the dent was minor and did not affect the internals, but I eventually got a lot less for the CD players.
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"None are so blind as those who will not see."