Nothing changes. You seem to be focussed on the execution of Buckbeak specifically, which I guess the movies portrayed badly? Here's the passage from the book. As you can see, they aren't actually around to see the execution.
Slowly, in a kind of horrified trance, Harry, Ron, and Hermione set off silently around Hagrid's house. As they reached the other side,
the front door closed with a sharp snap.
"Please, let's hurry," Hermione whispered. "I can't stand it, I can't
They started up the sloping lawn toward the castle. The sun was
sinking fast now; the sky had turned to a clear, purple-tinged grey,
but to the west there was a ruby-red glow.
... (some dialogue about Scabbers removed for length purposes)
They heard a door open behind them and men's voices.
"Oh, Ron, please let's move, they're going to do it!" Hermione
"Okay -- Scabbers, stay put --"
They walked forward; Harry, like Hermione, was trying not to listen to
the rumble of voices behind them. Ron stopped again.
"I can't hold him -- Scabbers, shut up, everyone'll hear us --"
The rat was squealing wildly, but not loudly enough to cover up the
sounds drifting from Hagrid's garden. There was a jumble of indistinct
male voices, a silence, and then, without warning, the unmistakable
swish and thud of an axe.
Hermione swayed on the spot.
"They did it!" she whispered to Harry. "I d -- don't believe it -- they did it!"
Later we see this scene from the other side, including the swish and thud of the axe. The very fact that the action is described using the exact same words is a clear indication that this is the same event we heard first time round.
"Where is it?" said the reedy voice of the Committee member. "Where is
"It was tied here!" said the executioner furiously. I saw it! just
"How extraordinary," said Dumbledore. There was a note of amusement in
"Beaky!" said Hagrid huskily.
There was a swishing noise, and the thud of an axe. The executioner
seemed to have swung it into the fence in anger. And then came the
howling, and this time they could hear Hagrid's words through his