The Levenshtein distance from duodenocholecystostomy to cholecystoduodenostomy is actually pretty high: 14. Transposing two contiguous chunks of letters has a high edit distance if both chunks are long.

A "good" anagram doesn't just have letters being moved a long distance, but also requires that the movements of letters be independent, something that Levenshtein distance doesn't measure.

The article gives an example, but to make it a bit more explicit: Levenshtein distance is a poor measure for the intuitive notion of how "non-trivial" an anagram is. Moving a chunk of letters together results in a high edit distance, but low complexity.

If you rank the entire list of anagrams by edit distance, the highest pair is "anatomicophysiologic" and "physiologicoanatomic", with an edit distance of 16 but a chunk score of only 3.

Because his distance measure is anagram specific and thus more appropriate than a general one.

(Technically speaking, a proper distance measure requires a distance of 0 for equal strings, so perhaps he should pick the number of splitting points rather than the number of resulting fragments.)