I would see this as an extension of the branch of linguistics called metalexicography which for decades has been examining people's use and perception of dictionaries and related works.
Practitioners of the field have long since noted phenomena which I think aren't in essence any different with modern electronic dictionaries/spellcheckers, whereby dictionary users believe that dictionaries are "seen as the repository of the linguistic 'truth' as opposd to actual usage" (Sledd and Ebbitt 1962)" or where there are "cases where dictionaries were used as evidence in a court of justice". Béjoint, via other authors, cites various examples, including cases where dictionaries were consulted by legislative bodies to decide whether a continental breakdast counted as 'board', or whether a T-shirt was classed as a 'souvenir'. The same author discusses how dicitonaries have also been seen as guardians of moral standards, with various words with sexual connotations appearing surprisingly late in dictionaries (p. 125).
If you look at people's use of word processor dictionaries and electronic dictionaries in general, I think what we're seeing is essentially an extension of this phenomenon. In times gone by, people would have worried a great deal that "The Dictionary" that they happened to have on their shelf happened not to include a particular word; now they instead worry that Microsoft Word puts a squiggly red line under it. And there are even still cases where users expect Microsoft Word's spellchecker to be some kind of bastion of morality: a glitch a few years ago, whereby the French word "anti-stress" was replaced by "anti-arabe", was not treated by some users as being a boring technical bug.