I am sorry for your loss. I have used Nation Wide several times over the last 16 years and have had no problem with them. However, I was shipping on the big air-ride vans from coast to coast. The haulers in the story sound like sub-contractors.
As a general rule, I dislike all horse shippers. They tend to be like gypsies and are completely unreliable. Part of it goes with the territory, but the experience can be variable. I’ve had a horse take 8 days to travel from Missouri to Virginia with one shipper. I had another shipper insist they were coming to pick-up a horse that was scheduled to be shipped by another shipper.
There ate lots of tales of woe and horror with horse shippers, unfortunately. And sometimes a good story or two!