No expert of the King family, but it does seem very obvious that Martha is wrong.
The William King who married (Nov 19 1864) Martha Parcel was a labourer and his father William was a malster
I started a free space page which I'm happy to hand over to you and you might find easier for research notes. https://www.wikitree.com/wiki/Space:William_King_Research
You could also use it to investigate the other William Kings to rule them out. It's a tough one. Probably finding his emigration would be a help.