No, that's not really the axiom. Guns don't jump up and rip throats out. Sure, there are "gentler" breeds that are responsible for more biting incidents. Labs probably bite more kids than most breeds. But that's a bite... Or a nip after an hour of being tortured by some little darling hanging on to his tail and whacking him in the balls with a plastic bat. As troubling as such a bite may be... It's just not the same as a dog who's whole ancestral history has been about fighting and killing. Not biting. -killing-. A lab will bite a hand, but a pit will tear a throat out. The difference is not subtle.
All dogs have the same instinct to attack the neck if they're in kill mode. Obviously, pit bulls are more dangerous due to their bite strength, lack of fear, and they're impervious to pain (I saw a pit bull attack a horse on Galveston beach, get kicked and thrown back about 15 - 20 feet, get back up and chase the horse down the beach). Plus, irresponsible a-holes tend to raise them to burnish their macho image. Mastiff's are giant Lion hunters (so the story goes), but they're some of the sweetest dogs I've ever encountered. But their size and strength make them a serious danger if they're unstable. Big dogs can, and do, big damage. Little dogs can be just as fearless and aggressive, but they're unlikely to kill an adult. Children - yes:
Since 1975, fatal attacks have been attributed to dogs from at least 30 breeds. The most horrifying example of the lack of breed predictability is the October 2000 death of a 6-week-old baby, which was killed by her family's Pomeranian dog. The average weight of a Pomeranian is about 4 pounds, and they are not thought of as a dangerous breed. Note, however, that they were bred to be watchdogs!
I "like" all dogs, but especially Dobermans, English Mastiffs (except they slobber and don't live long), most hunting dogs, and the Maltese.