The Sloughis, Salukis and Azawakhs come from Africa which is probably as far as the origins of the Labrador (Canada) than you get.
As Janneke said a greyhound is all about sprint muscle - the limit of their ability to run is because they would overheat if they needed to do prolonged activity as muslce produces heat when being used - even in Ireland and UK, not known for their temperatures above 20 when rabbits/hares would be in the fields for hunting. My ex-coursing greyhound mix would find a puddle in the coldest of days after a sprint to cool herself down.
The Azawakhs, Salukis and Sloughis need to be able to hunt in much hotter temps, mid to high 20s and probably more, therefore they cannot have either fat layer or the rounded muscle of the greyhound as they would suffer from muscle meltdown, even after a short chase, let alone an extended hunt.
Therefore their physiology has evolved to have the sparest of muscle (minimal heat generated, and maximum heat dissipated when exercising), which in turn means they can never get the well-covered look of our temperate climate breed dogs.
I would be devastated if we in the West change the most basic characteristic of these breeds simply because we don't like the look of it, either because its different compared to our temperate climate breeds, our perception of what is healthy has become so distorted because we are used to seeing fat as normal or we are too lazy to educate ourselves about what is different. I can well appreciate that these dogs do not appeal to everyone but surely that is no reason to change them?
I think some of these dogs that were thought 'too skinny' were immature which is why their bones are more prominent, they've yet to get their full muscle, sparse as it is, which adds shape.
Also I hate to see a fat layer on any dog - muscle yes, fat no. The fact that some folks starve any dog before a show just shows their ignorance, and laziness in not getting the dog into proper fit condition and using 'short cuts' to get the desired 'well muscled-look'. Rather than get the 'look', they should get the real thing! Their dogs would be much happier too I'm sure.