In X-Men Origins: Wolverine has Adamantium bonded with his skeleton, after Wolverine escaped the operating room, Col. Striker is given a gun and Adamantium bullets.
But according to the quote from the Marvel Wiki in the answer to the question Is Adamantium common?
The only known substance able to pierce Adamantium is the compound known as Antarctic Vibranium, also called "anti-metal"
So shouldn't the bullets have bounced off rather than penetrate the Adamantium skull?
Using information cleaned from this answer, I can tell you that yes it should have.
His bones have become laced with beta adamantium (at least at the time that Wolverine: Origins is filmed).
Adamantium Beta: The only known occurrence of Adamantium Beta was during the Weapon X Project. By the second part of the procedure when they laced his bones with Adamantium there was a reaction with his healing factor that bonded metal and bone. As a result the Adamantium "heals" just as his bones do.
Emphasis mine.
Two things to note from this:
I don't think there's an in-universe canonical answer to this outside of the quote you already mentioned. I think this is one of those times that Hollywood got it wrong.
You're right in that it shouldn't have pierced his skull It should have bounced. If a real bullet can bounce of a normal human's skull (which does happen) then even an adamantium bullet would bounce off an adamantium-laced skull.
I suppose an argument MIGHT be made that the shape of this particular bullet was designed to penetrate. it was tapered in an unusual way to increase the sharpness of the point, but still I doubt that would be sufficient. But I don't buy that, either. If adamantium can survive a nuclear blast intact, the paltry energy produced by a tiny amount of gunpowder would hardly be sufficient to overcome the strength of the adamantium. Again, it should have bounced, and bot the bullet and Wolverine's skull would show no damage.
Wolverine has fought villains that have Adamantium bonded to various parts of their bodies, for example:
Cyber's body was coated in Adamantium and Logan could not hurt him at all with his Adamantium claws. He had to find another way to take him out. His Adamantium couldn't pierce or scratch Cyber. Therefore, the bullet piercing Logan's skull should never have happened, but look at Deadpool in that movie; that shouldn't have happened either.
The answer is bad writing. The bullet should have just bounced off. His adamantium is bonded in way that allows his bones normal bio-functions to still work, (Probably cause after he was written as a character someone said ummm that would impede marrow and blood production) But its still indestructible metal, so no it doesn't heal. I always assumed his healing factor took care of that with the bones being encased in the stuff.
The amount of gunpowder in the casing would never have the force needed to penetrate it either. It was just a storyline brain fart so they wouldn't have to figure out how to film capturing, brainwashing him, and him escaping again. If they made a dart gun with a chemical made from Striker's son's brain to do the washing. Have them say they haven't perfected it yet, and it causes neural damage, chance of death etc. would have been way more believable.
It shouldn't matter whether or not the bullet would penetrate. Adamantium doesn't have magical properties that kill off people with healing factors. In the second X-men movie we see Wolverine get shot in the face by a cop with a normal lead and copper FMJ round when they were fleeing Bobby's (Iceman's) house. Granted the bullet should not have penetrated the Adamantium , but it did pierce his skull and it entered his brain, dropping him to the floor.
A few moments after we think he's dead, his healing factor pushes out the bullet and he returns to consciousness like nothing ever happened. An Adamantium bullet wouldn't do any different. And there is another factor that makes the Adamantium bullet impossible. The bullet would have to be able to conform to the grooves and lans in the barrel of a pistol or rifle.
A smooth bore shot gun would have worked for the Adamantium bullet concept, but not that revolver they had in the movie. Being Adamantium and being indestructible, the bullet would have gotten lodged in, and distended, the barrel and the gun would have blown up in Lauren's hand. Beyond that, the gun just happened to be in the appropriate caliber....not likely. The Adamantium bullet is a very weak point in an otherwise outstanding film.
To recap;
