You're right in that it is the user which makes the weapon deadly MOST of the time. However in the eyes of Dugu, The Sword is his sanctuary, his beloved, his companion, his everything. When he wields a sword, it no longer becomes just an ordinary manmade weapon. The sword itself becomes alive and divine.
Enlightenment, in the East, has always referred to the goal of all spiritual striving—the very pinnacle of spiritual attainment. When people think of enlightenment, they think of a spiritual peak achieved through Christianity or Buddhism. In the eyes of Dugu, The Sword IS his way of seeking spiritual awareness. When one puts as much dedication into The Sword as Dugu did, then they will have a chance at being called The Sword Demon. In Jin Yong universe, no one ever did. Bruce Lee once stated that martial arts is a form of individual expression. Yang Guo probably had the talent enough to reach the peak of swordplay if he devoted himself entirely to it but he didn't for his life is Xiao Long Nu. The Sad Palms is HIS martial arts expression. Dugu Qiu Bai's is the true way of The Sword.