Shielding can help with some aspects of electrostatic and RF interference, but MOST of our problem is with 60HZ AC hum that's in the air around us. The reason Jerry probably suffered very little from it was because of the stage environment he was so fortunate to live in. Concert settings and big venues like that have the great fortune to have clean power, a good distance from big AC transformer radiation, distance from or the non-existence of neon sign ballasts, etc.
Hum is in the air around us in nearly any club gigging or home environment, and all the shielding in the world isn't gonna make a single coil pickup not hum. It's the nature of the beast. As surely as they will generate signal from a vibrating string, they will also generate signal from magnetic waves in the air that pass thru them. You can't shield that stuff unless you encase yourself and your guitar in a booth made of mu-metal. You can help a tiny bit and you can reduce the high buzzy noises a bit, but 60Hz is there, so is the first harmonic at 120Hz.
Some tricks are to make sure your pickup is ideally close to the strings so that the strings signal is as strong as you can get it without compromising the tone or string pull issues with single coils. Higher signal to noise ratio. Also, having the humbucker option can save you at a gig. And then when you're stuck with single coils and don't want to sacrifice that sound, just stand with the guitar pointed in the best direction to reduce or eliminate the buzz. If you find that quiet position, know that a 180 degree rotation should give the very same null or hum cancel. It may not be the ideal position, but it's what Fender players have done for decades on stage or in the studio.
Basically it's ALL happening at the pickup. Hum is coming from the pickup and so is string magnetic/vibration signal. There's really not much you can do after that point to alter that ratio of hum/strings. It's embedded in the signal right out of the gate. One bonus is that Jerry tones almost completely dump the bass (60Hz) so the hum fundamental is pretty weak in a Jerry tone. So it's the buzzy components of the AC interference that can be helped with the shielding to some degree. But, fact is, it's gonna be there with single coils for most all of us in the real world with all those dimmers, neon ballasts, power line transformers, etc., and it changes from place to place. Some places have very little hum, some are nightmares. I can't tell you how many gazillion times I've had to pull the string on neon bar signs when playing a gig. Thats some of the nastiest noise you'll ever encounter. Fuck the Pabst sign in the window, I gotta play music, and I like my Dimarzio split to single coil tone!
... and it's just like any other day that's ever been...