In late September, she posted the following to the "Rumours" section on her website:
Snape was hiding under the Invisibility Cloak on the night the Potters died
No, he wasn't.
Well, that, as they say, is that. I say it cheerfully, because I wasn't totally invested in the "Snape under the cloak" theory, though I thought it should be raised. I raised questions then about the plausibility of such a scenario, and I guess it turns out it was even less plausible than I thought.
So we're back to the original question of the invisibility cloak's importance to the plot, and especially (potentially) to the night of Harry's parents' death. I think I'm going to stick by the possibility that Hagrid may have used the cloak in some fashion, on Dumbledore's orders.
Just watch: that one will show up debunked in Rowling's Rumours next! ;-)