To respond to Xachariah in my previous post summed up by "Enough people in the wizengamot would know about time travel that would be able to counter any time travel, or recognize it and have safeguards built in against tampering that way" This IS the universe where they don't use dying people to cast unbreakable oath spells, play Quidditch, and are sentencing a 12 year old girl to death in Azkhbahn after a 24 hour investigation (yes yes ten years but that would kill her all the time) If you look at all the possible worlds in regards to policies and safeguards regarding time turners worlds where Harry would be able to get away with this would have much higher probability density.