I just doubt that Joffrey would hand over something as precious as a Valyrian steel dagger
This bothers me too. On one hand, yes, Joffrey is remarkably stupid... but on the other hand, Joffrey is intensely conscious of status and any Valyrian steel blade is a status symbol.
There is also Tyrion's assessment:
A Game of Thrones - Tyrion V
Tyrion Lannister sighed. His sister was not without a certain low cunning, but her pride blinded her. She would see the insult in this, not the opportunity. And Jaime was even worse, rash and headstrong and quick to anger. His brother never untied a knot when he could slash it in two with his sword.
He wondered which of them had sent the footpad to silence the Stark boy, and whether they had truly conspired at the death of Lord Arryn. If the old Hand had been murdered, it was deftly and subtly done. Men of his age died of sudden illness all the time. In contrast,
sending some oaf with a stolen knife after Brandon Stark struck him as unbelievably clumsy. And wasn't that peculiar, come to think on it …Tyrion shivered. Now there was a nasty suspicion.
Perhaps the direwolf and the lion were not the only beasts in the woods, and if that was true, someone was using him as a catspaw. Tyrion Lannister hated being used.
I realize that KF is an opportunist who uses the mystery of the knife to redirect the weapon; but it is clumsy, not like LF at all. As for Joffrey, I'm not sure he cared all that much about his wounded pride or gave Bran a second thought. Cersei might think he was trying to impress his father; but killing the son of the King's Hand and the brother of your betrothed seems a bit of stretch to me.
It's the strangeness of the encounter as recounted by Catelyn that is curious to me.
A Game of Thrones - Catelyn III
When she turned away from the window, the man was in the room with her.
"You weren't s'posed to be here," he muttered sourly. "
No one was s'posed to be here."
He was a small, dirty man in filthy brown clothing, and he stank of horses. Catelyn knew all the men who worked in their stables, and he was none of them. He was gaunt, with limp blond hair and pale eyes deep-sunk in a bony face, and there was a dagger in his hand.
"No," Catelyn said, louder now as she found her voice again. "No, you can't." She spun back toward the window to scream for help, but the man moved faster than she would have believed. One hand clamped down over her mouth and yanked back her head, the other brought the dagger up to her windpipe. The stench of him was overwhelming.
She reached up with both hands and grabbed the blade with all her strength, pulling it away from her throat. She heard him cursing into her ear. Her fingers were slippery with blood, but she would not let go of the dagger. The hand over her mouth clenched more tightly, shutting off her air. Catelyn twisted her head to the side and managed to get a piece of his flesh between her teeth. She bit down hard into his palm. The man grunted in pain. She ground her teeth together and tore at him, and all of a sudden he let go. The taste of his blood filled her mouth. She sucked in air and screamed, and he grabbed her hair and pulled her away from him, and she stumbled and went down, and then he was standing over her, breathing hard, shaking. The dagger was still clutched tightly in his right hand, slick with blood.
"You weren't s'posed to be here," he repeated stupidly.Catelyn saw the shadow slip through the open door behind him. There was a low rumble, less than a snarl, the merest whisper of a threat, but he must have heard something, because he started to turn just as the wolf made its leap. They went down together, half sprawled over Catelyn where she'd fallen. The wolf had him under the jaw. The man's shriek lasted less than a second before the beast wrenched back its head, taking out half his throat.
"He came for Bran," Catelyn said. "He kept muttering how I wasn't supposed to be here. He set the library fire thinking I would rush to put it out, taking any guards with me.
I find the affect strange. He's battling visciously with Catelyn and yet his mind seems boggled to me, stupidly repeating the same thing. He's been hanging out in the stables two weeks after everyone has left. Only Hodor behaves queerly. Which might also be an indication that there is something more going on given Hodor's sensitivities.
"Who was he?" Catelyn asked them.
"
No one knows his name,"Hallis Mollen told her. "
He was no man of Winterfell, m'lady, but some says they seen him here and about the castle these past few weeks."
"One of the king's men, then," she said, or one of the Lannisters'. He could have waited behind when the others left."
and...
"It were no trick to hide from the stableboys. Could be Hodor saw him, the talk is that boy's been acting queer, but simple as he is ..."
So yes, I'm thinking that the House of B&W is involved in a way similar to the Alchemist using Pate to steal the key at the Citadel. And the reason why no man of Winterfell is so addlepated and hasn't run away with the knife and the 90 silver stags. The reason why
No one knows his name. The timing and the burning of the library tower coincident with the direwolves as protectors being kept from Bran's room.