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You would probably not want to use this if the function was unlikely to be frequently called with the same argument. You would DEFINITELY NOT want to use it if you need the function to return different results when called with the same argument...
This is a somewhat simple-minded check for English words which result in other English words when encrypted with the Caesar Cipher (and only using a shift of 3 characters). It considers a word valid if it is contained in the "common words" returned...
I'm also seeing an error on the webpage with the Genome data, although it works fine in Mathematica 12.1 desktop. The exercise 1.11 is taken directly from the GenomeData help page (in the "Neat Examples" section). Oddly, the example code generates...
I think that using "With" rather than "Block" to localize your "graphs" variable in Case 1 will give the desired result. (Of course, it's possible that I don't understand what your desired result is...)