What I meant by glossed over was the fact that until I started doing a bit more reading, I'd never even heard of the battle of Stamford Bridge, and it seems like a fairly important point, considering the fact that Harold Godwinson's forces had to march north to face Harald Hardrada's Norwegian invasion, then straight back south to face the Normans. From what I've read, this was one of the deciding factors in William's victory.
I've also read some speculation that Harald and William had made an agreement to invade simultaneously and then split the newly conquered land between them, but William decided that by waiting and letting Harold face Harald first, he could more easily defeat Harold and then take the whole thing for himself. No idea if there's any truth to this, but it doesn't sound like it's beyond the realm of possibility.