The End of Time - The Master shows up, and the Time Lords are trying to come back. The Doctor knows that they're 'stuck in a time bubble' and will destroy everything if they come back. So he puts them back in the bubble.
Okay, so here Gallifrey and Skaro and the time war and everything related to it is "timelocked" so there aren't people traveling to or from the time war mucking things up. If it wasn't timelocked, there would be nothing to stop anyone from leaving it - and then everyone would leave it - and then you'd just have the war all over again. The High Council is trying to get out of the war here by escaping through the Master. If you pay close attention to The Day of the Doctor, they say "The High Council's plan has already failed" or something close to it. This plan was what we saw in The End of Time. This happens, for the timelords, BEFORE the Doctor uses The Moment, and as such, BEFORE Gallifrey was destroyed. They shouldn't have been able to escape the timelock, but the link in the Master's head made it possible.
The Name of the Doctor - John Hurt shows up and suddenly the Doctor remembers destroying Galliffrey, which he remembered being time locked 3 years earlier....
He's always remembered destroying it. Like I said earlier, the time war was time locked, but ultimately, Gallifrey itself was burned.
The Day of the Doctor - ok so after all he never destroyed Gallifrey, and saved it by sending it to another universe. Fine. But then he wouldn't remember, as 10th, that it had been saved (even less locked in a time bubble), as he would lose his memory of what happened, until it actually happened. Starting to get lost there. Oh and he's very excited to go 'home', nevermind that 3 years earlier he tried to send the Time Lords where they were so they wouldn't destroy the universe.
This relies on assuming Gallifrey was timelocked and not destroyed, which I already explained earlier. So, based on that, we have a timelocked war, and a burned Gallifrey. Hurt/10/11 are all in on saving Gallifrey, but since it's a multi-Doctor story, only 11 will remember trying to save it instead of burning it. When there are multiple Doctors in a story, all but the last one in the timestream forget the events. They may have a slight feeling about something echoing through time, such as 10 saying "I don't want to go" about Trenzalore and repeating the line just before regenerating. But their memories are basically wiped of the events. Hurt/9/10 can't have possibly known they tried to save Gallifrey, which is why 9 and 10 still feel/act like they did in their runs. They simply don't know. 11 remembers he tried to save it, but that's all he knows - they tried. When the three of them arrive back in the gallery, they state as much - they tried but they simply do not know if it worked.
That's when we get to the Curator. Hang on tight. The Curator may or may not be a future incarnation of the Doctor. But, let's assume he is, since it was HEAVILY implied. He told 11 that the painting was called "Gallifrey Falls No More" which means he DID save Gallifrey. But guess what? This is a multi-Doctor interaction, so 11 cannot remember this bit of information. His memory basically stops when Hurt and 10 leave, as if the interaction with the Curator never happened. So we're stuck with maybe it's burned, maybe it's saved in a pocket universe, but nobody knows for sure.
The Time of the Doctor - he's suddenly scared of the Time Lords again and doesn't want them to come back. And he seems not to be so sure he actually saved them. Then he stays in that town for years protecting it from daleks who are attacking to make sure that the Time Lords don't come back, when apparently the Doctor had no intention of letting them come back anyway...
Gallifrey is in a bubble universe (think like the universe in The Doctor's Wife), and it's smashing its universe against the Doctor's universe in an attempt to make a return. As a result, the scarred-over cracks in the fabric of the universe have reopened. These are not the SAME cracks, but different cracks in the same places.
The Doctor's not scared of the time lords. He says they'll come back in peace. He's scared of what's waiting above Trenzalore if the timelords return. Everything that ever hated the timelords is waiting for them, thanks to their ****-poor idea of sending a signal through all of time and space. So if they return, the war is basically waiting right there for them. So they can't come back, not here, not now, or the time war will start again. He wasn't sure he saved them due to the multi-doctor-memory-wipe-thing I just explained.
If there hadn't been a sky full of enemies, you can bet the Doctor would have let the Timelords back in. But he couldn't, because they would be destroyed anyway.
He had to stay, because if he left, the shield around the planet would be broken and all the baddies would get in. This is exactly what happened when he and Clara left for a bit. He came back, and he came back to war.
I will bet you anything we'll find Gallifrey in the next series, and the timelords will return.
Sorry, but WTF is Moffat smoking? Or am I totally missing something, considering that I haven't seen anyone else that it seems to bother?
I'm not going to argue that Moffat is Moffat, because he is. But I hope my explanations helped a little. It takes a lot of rewatching and really trying to make headcanon work to get it pieces together, but that's half the fun