I don't think that follows. The LHC is many, MANY orders of magnitude too weak to produce this kind of thing, but it can produce beams of many protons or, alternatively lead nuclei. Thus, it could conceivably create entirely different effects.
The same logic applies to the argument that any black-holes or otherwise dangerous particles would simply zip by the Earth (stated in a sibling comment to yours). Particles of slightly lower momenta come in higher numbers, so these would produce the dangerous particle, but not retain enough momentum to escape. Since the Earth has not been destroyed, there are no particles produced at low enough energies for us to destroy ourselves.
See, for example: http://www2.astro.psu.edu/users/nnp/cr.html.