"... It's probably just a hair. It's probably just a hair. It's probably just ..."
The "never more than three feet away" thing seems to have originated in 1995 when arachnologist Norman Platnick began an article with "Wherever you sit as you read these lines, a spider is probably no more than a few yards away." Which is technically true, especially if you keep in mind the "probably" modifier. But, as the years went by, the line was repeatedly misquoted by other articles, evolving into "Scientists estimate you're never more than three feet from a spider." Even Platnick misquoted himself in a CNN interview, saying that "You're probably within seven or eight feet of a spider, no matter where you are."
Above: Dr. Platnick, proving his point.
If you're standing in a lush grass lawn, then yeah, there might be tiny, harmless spiders right under your feet or as close as a few centimeters. If you're in parking lot, on the other hand, the closest spider could be as far as 100 feet. If you're in a jet over the ocean, the closest spider might be a ballooner getting sucked into the engines. So you probably do pass by a lot of spiders without ever even knowing it, but there's no scientific claim or study that ever said you were always within a certain distance of one.