With regard to the sociological note. It's a half truth. H.G. Wells wrote about something similar to atomic bombs in a 1914 novel (The World Set Free) when there was no understanding of how an atomic bomb would actually work. In fact, there are newspaper articles from the 30's reporting about the wondrous possibilities of nuclear energy. Strangely enough, Leo Szilard, the man who hypothesized the chain reaction as the real basis of a nuclear weapon, read that book a year before his discovery. This was 1933. Mainstream acceptance of the possibility of a bomb was not until after the first fission was actually achieved: 1938. The bomb project began in 1940. Around this time, Niels Bohr (that Niels Bohr) estimated that building a bomb was a practical impossibility as it would require the industrialized output of most of a nation to get sufficient amounts of enriched uranium. He concluded it could be done but only in far future (much like an antimatter bomb). When he joined the project and saw the shear amount of resources the American's were devoting to the project and the advances being made, he changed his mind.
For instance, after spending roughly the cost of the LHC on the first uranium separation facilities at Oak Ridge, (fun fact: a significant portion of the USA's silver coinage reserve was melted into calutron's for magnetic separation) the facility, which consumed about 15% of United State's electrical output, was producing about a pound of U-235 a day, enough for a bomb every 6 months.
The LHC or ALPHA is like a mass spectrometer. It's a scientific tool. Technically, you can also use a mass spectrometer to enrich the uranium to make an atomic bomb, but it would take about a million years to make enough. See the similarities?
It is a bit disingenuous for CERN to say "we" can't make antimatter bombs. If "we" means CERN then it's absolutely true, but to comment in an overall sense of "we" would be yet another foolish misunderstanding of the abilities of an industrialized nation to accomplish something when incredibly dedicated to it.
The real reason we won't see anti-matter bombs is in CERN's quote though. A hydrogen bomb is plenty "good enough".