I've held that the Invisibility Cloak has got a lot more going on with it than an easy way for JKR to allow Harry to get around the castle unnoticed. It seems to be too much a part of the story and plot progression for it just to be a cloak that Harry gets for Christmas becuase DD has been keeping it for him. Somehow, DD got a hold of it, held onto it, and knew full well that Harry would use it both for protection and to get himself into trouble.
What if it's got something to do with Snape and Godric's Hollow? Perhaps Snape will be the one to finally give us an accurate account of what it going on. His prescence at Godric's Hollow would explain how DD found out and why there was a delay in Harry being taken to the Dursley's home. What if Harry was under Snape's protection before Hagrid's? While Hagrid doesn't necessarily like Snape, I can't think of an account until HBP when the DEs set his hut on fire that there had been much interaction or confrontation between them. Did Hagrid question Harry when he (Harry) told him (Hagrid) about his questions about Snape? Did Harry even ask Hagrid?
I think Hagrid definitely knows more about the relationship between Snape and Dumbledore than he is letting on. Dumbledore always trusted Hagrid with his most important jobs, after all.
I found in interesting that at the end of HBP, Hagrid doesn't talk about being angry with Snape or wanting revenge. Who, besides Harry, was more loyal to Dumbledore than Hagrid? Who is about the only person in the books more impulsive and emotional than Harry, if not Hagrid? But Hagrid isn't talking revenge. He's just mourning Dumbledore.
Which makes sense if you believe the theory that Dumbledore knew all along that he was going to die from whatever curse had blackened his hand, and that Snape was just "killing" Dumbledore to keep his cover and protect Draco. And that Hagrid knew about it.
I like the idea that Snape was at Godric's Hollow that night, because I think it gives Snape a more compelling reason to feel remorse than just hearing about what happened. Much the same way Draco could boast about being given the task of killing Dumbledore, but fell to pieces when the moment came to actually do it - I could see Snape thinking he could "get back at" James by serving up his family. But when he actually saw Voldemort kill them, saw Lily fighting for her life, saw Voldemort try to kill baby Harry - then he was horrified and repulsed. Snape would have been only 20 or 21 at the time - not much older than Draco in HBP.
Heck, I will break my own rule and say that "what if" Snape were there and "what if" Snape did indeed pull baby Harry out of the house and take him to Dumbledore. That would certainly be a more compelling reason for Dumbledore to trust Snape than Snape saying he was really, really, sorry.
I'm not sure where the Invisibility Cloak fits in there - unless Snape took it when he took Harry, and gave both to Dumbledore.
That's about the most farfetched theory I have ever come up with. I think it might sound too dramatic. And it doesn't explain why Hagrid would tell Dumbledore that the "house was nearly destroyed" when they met on Privet Drive the next night. Unless Hagrid was sent to confirm the story or look for clues or something?
And it's hard to reconcile Snape still hating James so much and being so mean to Harry, if he is really that remorseful.
Hmmm...I think I will have to do some re-reading before I commit to this idea.