It was, as the Normans themselves admitted, conducted "over hidden relics" and no witnesses for this 'oath' were ever named- was it a public oath- and in the open air(Bayeux tap)?
English custom was that they were always sworn on a gospel book, (Normans say Harold swore manibus junctis- feudal fashion) so was it 'under duress' or procured by deceit, which would render it worthless anyway, certainly outside of Normandy?
William of Jumieges never went as far as stating that Harold had sworn what later the Normans said he did.
Normans had drive and ambition- also a voracious reputation for chicanery and inventing outrageous claims- Dudo of St.Quentin- historian of the early dukes- had the gaul to state that William Longsword and Richard the Fearless reigned over "half the world".
Was William's daughter -Adeliza- 'promised' betrothal to Harold? A way of binding him to the duke, whatever, this seemed to have fallen through (did Harold refuse?)
The Normans state that Harold coveted the crown himself – even if true, why would H willingly and freely swear this oath, thereby ruling HIMSELF out of the succession as the most qualified candidate in or out of England, socially and Politically?
But instead a storm blew his embassy off-course and unluckily into William hands (via Guy of Ponthieu) and, knowing all too well his possible fate as a 'guest'/captive, grim gaols that meant a death sentence and penchant for brutality- especially poisonings, (a nephew of King Edward, earl Ralf's younger brother, Walter, Count of Mantes, and his wife, died prisoners this year in William gaols- poisoning rumours. But the two nobles were never seriously considered by Edward as successors)
William’s father Robert ‘the Devil’ had been suspected of poisoning his own brother Richard, after all?
Harold seems, in my view, to have gone along with the deed whilst as a Norman "guest" for his own 'safety', of his entourage and that also of long-term Norman captors and kinsmen Wulfnoth & Hakon etc, knowing how worthless the "sworn oath" meant in English eyes and how he could easily shrug it off when back home, under English law?
Only the King & Witan could decide the succession- not some 'hidden' Norman verbal oath- esp under duress (only the Normans ever stated that Harold was in any danger!), thus invalid in English contemporary eyes!