Except the NYT magazine article author makes it quite clear that she is chemophobic, with repeated statements about her fear. Here's a direct quote: "It reinforced an image of Shepherd as sick, forever dependent on a drug I felt afraid of, however unreasonable a doctor might tell me that fear was." Similarly, when a doctor suggests increasing the dose of methotrexate she panics.
I guess I still don't see anything there that could be construed as 'chemophobia'. She doesn't want her kid to self-identify as sick or to die of liver failure. I don't see how either of these concerns are crazy or anti-technology or whatever. Especially since in the beginning she says she was excited about the diagnosis because it meant they could try different drugs.