Skirmish for Battle Hill, 1066?

Supposedly, having been detected on Caldbec Hill by the screen of alert Norman scouts, King Harold ordered some of his men to dash ahead of the main army and seize the high ground on this strategic hill (2m north of Battle Hill -the usually accepted battle-site).

Likewise, Duke William sent forward some of his own men, especially his crossbowmen whose bolts so terrified the inexperienced fyrdsmen that they withdrew to the ranks of the main army. Luckily the huscarls were tougher and had seen these type of enemy soldier before, and they took the hill.

William of Poitiers stated that a large Danish contingent was at Hastings (presumably either allowed by Harold's cousin King Swein of Denmark to be present, or were they also mercenaries like many housecarls and French/Breton/Sicilian/Normans?) that they deployed on higher ground on a hill near to the wood from which they(the English) had emerged.

Was this the resulting pre-battle skirmish (above)?