According to http://www.worldwidewords.org/, most dictionaries consider “gainsay”–meaning “to deny or contradict”–to be formal or literary, and some categorize it as archaic. Obviously in 1914 it was in common enough usage for Mary Roberts Rinehart to put it in the thinking mind of her protagonist.
What happened to “gainsay” between 1914 and 2014? Why would a perfectly clear and succinct word disappear from our speech and from our casual writing?
The After House, by the way, is not classical Mary Roberts Rinehart but is an excellent mystery.