Air Canada - They have an excellent reputation for transporting pets.
I don't know where you get your information from, other than their own employees, but I can tell you that I travel extensively in North America and overseas. When situations permit, I take my dogs with me. One of my dogs has been on a plane at least 15 times.
One of the worst carriers in the world for pets is Air Canada. Period. (Sorry AC)
and the pressurized cabins are only available on "some" planes on "some" flights. If the dog is small enough pay the extra $$$ to have it travel in the cabin and NOT in the cargo hold.
My experience has been that the very, very best is KLM.
I think that the person wanting to use Delta should find out more information - they can't be any worst than AC.
FYI - air travel for pets can be an ugly experience or of course a passable one, but never a good one. Most seasoned pet travellers will tell you that while pets can get used to it, they are usually not too happy about the entire prospect, but a re no worse for the wear. Our last flight was a nightmare (AA) and I vowed to not ever put Merlin on a plane again if I didn't have to. HE stays home now - or - I'll spend the extra and purchase another full ticket and take him on the plane with me.
Other than KLM, the airline industry's cargo pet transport system just isn't up to scratch yet at all.