The point is that you can exactly recreate a particle including its entire quantum wave function (preserving uncertainties) from one place to another without "existing" in between. That's why it counts as teleportation: you get the same object, not a similar object but the same object all they way down to quantum fluctuations, at a distance.
That actually isn't how this works. Yes, you do have two objects with entangled wavefunctions but that isn't remarkable at all. And the entanglement occurs when the objects are created at the same place, and then they proceed to the measurement points using entirely conventional slower-than-light means.
Its only a single bit, the polarization of the photon, that is found to have been determined in both places simultaneously. Its true that this is a new piece of information that arises in both locations simultaneously, but since this is a thing that appears in two places rather than something that moves from place A to place B I'd argue that the term "teleportation" is pretty misleading here. After the measurement the measured particle is hopelessly entangled with the measurement apparatus and through that with the surrounding universe, so the unique link between the two particle is hopelessly broken at that point.
found to have been determined in both places simultaneously.
That's not true. You measure one of the qubits, and its state is destroyed, randomly scrambled. When you transmit the information and apply it to the other qubit, it now has the same polarization as the first one had, before. You still don't know what the polarization is though! The entanglement is still intact, and you haven't made a measurement of the system (as a whole) so the wavefunction has not collapsed. http://en.wikipedia.org/wiki/Quantum_teleportation#Remarks
Oh, huh, the process described there is distinct from the sort of "Quantum Teleportation" that I was used to. Using an entangled pair and some transmission of classical bits to transmit a qubit across a distance is pretty neat, and this "quantum teleportation" really is quantum teleportation. It's only sort of related to the cryptogrpahic technique I'd previously heard described as "quantum teleportation", but in the absence of evidence as to who grabbed that pair of words first I won't complain.