The phrase "broadest backs" refers to people who can handle and endure difficult situations or responsibilities. It implies that these individuals have the strength and ability to support others and carry heavy burdens. Full definition
I've figured out that all my weight lifting has given me a much broader back than I'm used to. (looplooks.net)
(1) The XYZ is a strongly built, medium - sized, short - coupled dog possessing a sound, athletic, well - balanced conformation that enables it to function... Physical features and mental characteristics should denote a dog bred to perform as an efficient... The most distinguishing characteristics of the XYZ are its short, dense, weather resistant coat... a clean - cut head with broad back skull and moderate stop; powerful jaws... (petpeoplesplace.com)
The most distinguishing characteristics of the Labrador Retriever are its short, dense, weather resistant coat; an «otter» tail; a clean - cut head with broad back skull and moderate stop; powerful jaws; and its «kind,» friendly eyes, expressing character, intelligence and good temperament. (akc.org)