I love my Tele, but it did need some extra shielding to reduce the levels of hum and static. I have it down to acceptable levels, but it's still definitely a (minor) issue. I accepted that some hum was inevitable. 
Until I got my FGN. This thing is utterly silent in terms of buzz and hum, whether I'm touching the strings or not. Whether I have it split or hum-bucking. No hum. Nothing.
So it is possible to completely eliminate it. Now I'm on a mission. Mega-shielding is coming up. And some research regarding best earthing strategies.

Until I got my FGN. This thing is utterly silent in terms of buzz and hum, whether I'm touching the strings or not. Whether I have it split or hum-bucking. No hum. Nothing.
So it is possible to completely eliminate it. Now I'm on a mission. Mega-shielding is coming up. And some research regarding best earthing strategies.