The Shadowscales can be considered a form of change/rebellion/source of upheaval as they can be hired to remove people stagnating in positions of power (though rhis actually fits the Dark Brotherhood more neatly and could be whu Shadowscales were sent to them). They essentially do what Sithis is ( chaos itself) and by doing that they are his hand on Nirn.
The Argonians worship the Hist, and the Hist respect Sithis: "It is believed that the Hist acknowledge Sithis' role as the Original Creator." (en.uesp.net/wiki/Lore:Hist)
The reason for Argonians born under the shadow becoming Shadowscales is likely because of the fact that those born under the shadow are extra sneaky and can become invisible. Such a gift would be quickly attributed to Sithis in a society that reveres him.
The Dark Brotherhood would be quick to snatch up assassins with such natural talent. The deal between the king of Blackmarsh and the Dark Brotherhood would be mutually beneficial, the king of Blackmarsh gets the Brotherhood's services, and the Brotherhood gets some of Tamriel's most effective assassins.