The comparison using a single "not"
Solution 1:
Yeah, it's a neat shortcut for saying "51% or more X". And like the other answer states, the sentence you quote is a bit tortured - it's not the clearest writing. One reason is because of the "double negative", something we try to avoid. I had to pause for a moment to figure out what its author meant. And yes, also, it's sometimes said in an ironic way. Although, "more often than not" is just fine and common. It's a longer way of talking, so it goes well with a beer in one hand and a pool cue in the other.