Does physics allow for a machine that copies an object with 100% accuracy?
The answer depends on what aspects of the object you are copying.
If it is only the text of a text file that you are interested in copying with 100% accuracy, then the answer is as simple as
cp old.txt new.txt. If you want to copy all the metadata including filename, then you could do
cp old.txt ../anotherDir/old.txt. If you want the full path copied with 100% accuracy then you need to move the file to another filesystem. If you want to copy the entire filesystem with 100% accuracy, then you need another partition. If you want to copy the contents of the drive with 100% accuracy then you need another drive.
The digital assets are the trivial example, but I mention it to show that the question itself is not well-defined. If you want to copy the physical drive itself with 100% accuracy then you could run another drive off the assembly line. You could argue that is not 100% accurate as the dust particles on the case might be arranged differently, but I would then argue that is not part of the drive itself. Everything that is "the drive" is what came off the assembly line and any variation therein is still "the drive". You could then further refine the question to putting the drive in a box and saying "clone everything in the box" to which we would have to ask if the state of the nitrogen, oxygen, and CO2 molecules in the air are to be copied as well.
In short, you would have to define the boundaries of what you are measuring to decide if it could be reproduced with 100% accuracy. As Manishearth mentions, you will never reproduce the quantum state. If you are not interested in the quantum state but rather some other arbitrary value of interest, then you could in theory sufficiently reproduce the object with 100% accuracy for what you are measuring.
Classically speaking, yes. Classical mechanics doesn't forbid this from happening, though it doesn't prescribe a way of doing it either.
If we take into account quantum mechanics, however, you can't. The quantum state is something that cannot be fully copied over, due to the no cloning theorem.
Most matter has a non collapsed quantum state. The electrons in an atom are in a quantum superposition in both position and velocity spaces. There is similar quantum behavior at the molecule level, especially if there are currents involved.
Now, if an object had all quantum states in its eigenstates (i.e. no superposition) -- then this would be possible. However, due to the Heisenberg uncertainty principle, it's not possible to simultaneously know everything about the position and momentum of particle. So we can never truly have such an object, and no object can ever be copied perfectly.