Yeah, really. They were originally named "Wil Wagner and The Smith Street Band" as a direct reference to Bruce Springsteen and The E Street Band, and shortened it when they changed their songwriting style away from having the titular Wil do everything, over to more of an all-in collaborative process.
By funny coincidence, I also saw them live with AJJ last year, I think in September, but in reverse order on the billing. AJJ were opening up for them at their "I Love Life" festival down here, at their Brisbane Hotel gig, along with The Sugarcanes and some punk mob I don't remember the name of. It was kinda funny, about half the crowd went absolutely apeshit for AJJ, the other half were like "Who the fuck are these dudes?"