I'm sorry, I don't know how much more stripped down you can get with Green Day than ONLY TWO RHYTHM GUITAR TRACKS. I mean, you could only have one guitar playing everything (rhythm parts, solos, the whole nine yards), but that would sound too hollow and hollow's not the band's forté. And as for the "polished" and "over-produced" sound of the record(s), that can simply be attributed to Chris Lord-Alge's mixing style. He just likes to mix big. Nothing wrong with that.
But nonetheless, the music sounds plenty garagey! Stray Heart's very vintage, same with Stop When The Red Lights Flash. How about Wild One, which is something you'd expect to hear at a 1950's Sadie Hawkins dance. And you can't get much more vintage and bluesy than Lady Cobra! That song's basically a Chuck Berry song on steroids!! True, there are a couple not-very-vintage songs like Baby Eyes, Ashley, and Nightlife, but overall, it's very vintage and garage-rock.
And also keep in mind Billie was talking about it being "garage rock sounding" in relation to the other two records, so in that respect, he's right.