This is correct--- you need a few KeV to break the Coulomb barrier and allow fusion. But a few KeV is still well above the energy of ordinary chemical reactions, and well above the energy of thermal motion, so at ordinary temperatures, when the typical thermal energy of a molecule is about 1/30 eV, 3KeV is 100,000 times bigger, it's just enormous. There is no probability of getting KeV's in a single particle through thermal motion.
Still, 3KeV is the energy of inner shell electrons, and inner shell dynamics can conceivably be responsible for cold-fusion--- the no-go arguments are all circumvented when the inner shells are excited. This shows that the standard theoretical arguments against cold fusion are no good, but it doesn't explain cold fusion by itself.
There are a handful of beam experiments, where people shine a beam of deuterons at energies of 1-20 KeV into a deuterated metal, and look for signatures of fusion. These experiments are notable, because there are unexplained enhancements in the fusion rate at low beam energies, by a factor of about 3 or so (not so big by cold fusion standards). The actual beam measured cross section for hot-fusion is still too small to be responsible for cold fusion, but cold fusion can't be hot fusion anyway, or Pons and Fleischmann would have died from the neutron flux.
In cold fusion, the major mystery is how you output alpha particles without neutron emission. Since this process violates momentum, it requires a spectator body, a spectator electron or a spectator nucleus, to picks up the energy momentum electrostatically. But a spectator electron has a small charge, and a spectator nucleus requires the fusion intemediates to be close to the nucleus. But order of magnitude estimates don't rule out the thing immediately, and some idea must work, because the experimental data is so overwhelming.