That has a lot to do with having two amps, I'm pretty sure he keeps the Twins clean and distorts the Silvertones. Not 100% sure, I'm sure there's someone far more obsessed with him than myself. Also, contrary to popular belief, they Stripes do use lots of layering, overdubs, and subtle studio tricks (I discovered this today while analyzing their first record in my car today during a long and boring interstate excursion).
Telecaster - SG - Jaguar
Princeton Reverb, Extra Reverb
P-Bass - Mustang Bass
Apogee Duet 2 - Ableton Suite
Yeah, I started noticing the overdub here recently, as well. That seems a viable explanation as to how he gets those high notes in there. Never thought of that way. I know all his stuff is probably custom tweaked, and those Silvertones play a big part.