I'm honestly not even a really huge fan of the bands you listed that inspired the Silversun Pickups.... Although, I mean, I do have all their albums on my ipod. Charlie XCX is playing here in LA in a month but she's playing at the Troubador which I'm not a huge fan of.
And no, Handsome Furs have absolutely no relation to the Psychedelic Furs. Dan's collaborated with a couple of artists - for instance, he played a few tracks for Islands - but the only direct correlations the band has would be that Dan was in Atlas Strategic, Wolf Parade was initially just him and Spencer Krug, Handsome Furs, then Divine Fits.
Side note, you know those people who say they aren't that into music? I don't get it. To take it a step further, I went on a blind date with this girl and started talking about music, what I played, and the process of writing a song then she just kind of laughed after saying she didn't get it. I don't think I've ever been so turned off by such a hot girl so fast.