IIRC, it’s from a time when storytelling was done around the kitchen table while mom or grandma was cooking, typically stirring the pot with a wooden spoon.
Ummm, no. The name arose because Barbara Hamel (later Mikkelson) was famous for threatening to paddle miscreants on the Usenet newsgroup alt.folklore.urban with a wooden spoon for their misbehavior.
Please see this thread where Barbara Mikkelson herself is quoted as saying
"The Snopes were a family of characters weaved throughout the works of Pulitzer Prize-winning American writer William Faulkner. When David Mikkelson, creator of snopes.com, first came onto the Internet in the late 1980s, he worried even back in those relatively uncrowded days that no one would remember yet another David. He was thus inspired to adopt a nom-de-Net, selecting one that honored those fictional Faulknerian characters, and began signing his newsgroups posts as “snopes.”
Over the years snopes established quite a fearsome online reputation for his ability to thoroughly research and debunk false claims. When it came time to name our domain, www.snopes.com seemed the obvious choice."