What it reminds me the most of is Harry’s discussion with Hermione about the need for heroic responsibility—about always shouldering the responsibility for any final outcome of events, instead of thinking that your job is done when you, say, go to Professor McGonagall and tell her to do something about it.
My guess(though I wouldn’t assign a very high probability to this) is that it will be uttered by Harry while he’s away from anyone he considers to be sane or responsible(like, say, Quirrell) and he fails to prevent something tragic from happening. A more specific hypothesis: Quirrell’s identity is revealed by him doing something unspeakably evil and Harry blames himself for not piercing the disguise earlier.
Re: Flamel and his open-secret-recipe for the Philosopher’s Stone.
Here’s a quote from chapter 61:
And yet, the recipe is openly available for everyone to see. If anyone could reproduce the stone from the recipe, it would be the very intelligent, rational(and very interested in immortality) Voldemort.
So, how do we reconcile these two facts?
One option is, of course, the published, known recipe is a fake. The stone is real but Flamel lied to everyone about the recipe. That’s certainly a plausible—if boring—explanation of the facts. The other plausible explanation is as Harry says—maybe the stone is a fake. Maybe Flamel is immortal because of Horcruxes and he invented the stone as a way to keep people off the trail of his phylacteries. Maybe Flamel isn’t immortal at all, maybe he pulls of a Batman Begins Ra’s Al Ghul style of immortality. Any of a dozen options is possible.
However, if we take things at face value, I think we can end up with a more interesting conclusion—I think this might be our first piece of evidence(it’s not very good evidence, but evidence nonetheless) that the Interdict of Merlin is an actual, real magical effect, rather than just a cultural thing or a legend. The reason people can’t reproduce the stone is because the Interdict obscures some part of the recipe.
I guess this is testable—do we know if Flamel had any apprentices to whom he tried to personally explain how to make the Stone?