DNA methylation means adding one or more methyl groups to the DNA, so technically it is an alteration. But most people would assume that altering a gene specifically means changing the "letters" of the gene sequence that encode the protein, and that's not what DNA methylation does.

I can't speak for every institution, but our PR department does as many back and forth passes as it takes for the scientists who did the work to sign off that any edits made still preserve scientific accuracy.

Describing a change to DNA methylation "alters" a gene is technically correct in the sense that it is an change to the molecular structure of the DNA that makes up the gene, but is indeed misleading, because without further clarification a majority of people would assume it refers to a change in the gene sequence.

Imagine you have the text of a book in a word processor. You can change the text by typing new words or deleting ones that are there. You can also change the font, size, alignment, etc. The latter category of changes does not alter the words in the text, but it can affect how that text is interpreted, which parts of the text a reader focuses on, etc. The difference between a genetic alteration and an epigenetic alteration is conceptually similar. Genetics is changing the "text" of the genome while epigenetics is changing aspects of the genome that affect how that "text" is interpreted and used.