[quote=@Emma]
Almost everyone is illegitimate. 

[b]King[/b] - "Send me the [i]Heirs[/i] of your house to be my wards!"

[b]Everyone[/b] - "Here is are bastards, that can't inherit....Mwhahaha"
[/quote]

Well think about it like this: the King, who isn't overly popular in the realm, asks for each house's rightful heir brought to King's Landing. For some reason. Anyone could interpret that as the Tarygaryens holding them captive as a detourant. Not only that but the Tarygaryens could have a reasonable Cacus Belli for war if a house proves to be a little too rowdy.