I think it started during the filming. We got pictures from Home Again, if I recall, but they were blurry, and Scully was wearing a necklace with what looked like a ring as a pendant. After trying to zoom in on the pictures, we all got convinced it was a wedding ring, and then David perpetuating the legend during interviews and comic cons (If you haven’t read it already @sunshinetoday just made a great answer to this same ask with all David’s married/not married quotes : http://sunshine-today.com/post/164216499442/what-is-the-wife-gate ).
Actually, no one said they’re not really married.
Just Holding Hands 