The way I understand the situation in 1066, Harold Godwinsson was crowned king in 1066 by the highest legal authority of the time, in that he was elected by the Witan and anointed under God. Compared to Harald Haardrada and William's counter claims that they had been promised the throne by a previous king.
Clearly, the lords of England did not feel that William's "rightful" claim was sufficient, and his subsequent conquest of England rendered that a moot point by replacing the lords with Norman adventurers of his choosing.
Was there a social, or legal framework in place that meant that William needed a right beyond the right of conquest?
I think I might be able to shed some light on the situation.
One element of the Norman Invasion that is often overlooked is the involvement of the Pope. Long story short, the English Church had retained a certain amount of autonomy from the Central Church in Rome, and this meant that many customs, practices, etc. were considered dangerously 'out of date' with the mainstream church.
Why is this important? Essentially William was quick to grasp the political ramifications of Canterbury's differences with Rome. Alongside the Archbishop of Rouen, William played up the unorthodox practices of the English Church, as well as the holy nature of Edward the Confessor and Harold's oaths to make William the next King. The Pope saw this as an opportunity to reassert Papal authority over what he saw as a distant and slipping Church.
Thus a deal was struck - William gained the legitimacy provided by Papal authority (essentially the highest authority in Medieval Europe - higher than the Witan) and the Pope gained more control of a wayward Metropolitan.
It should be noted that William is cited as having flown Papal flags over his army at the battle of Hastings, further evidence that he took the Papal mantle (or at least the legitimacy it conferred upon his invasion) seriously.
Best book I've found on this I've read was Frank Barlow's Feudal Kingdom of England, 1042-1216. It's a little dated but gives a good background for the era!