Not only is Back In The USSR blues-influenced, it's a short step away from being a 12 (give or take a few) bar blues. Instead of the original chords
A D C D
A D C D
A C D D
try singing the verse and chorus over a 12 bar pattern
A D A A
D D A A
E D A E
The melody and harmony reinforce the blues style ambiguity. The blusified melody (Ticket 22) created from the minor pentatonic scale (A C D E almost exclusively) implies A dorian when heard over the D major chord. The A major root chord (not A minor) clearly heard in the piano part suggests A mixolydian. The E7 chord (Ticket 65) in the intro and bridge pulls us towards A major. This 'modal' feel (“we're definitely in A but we just can't settle on a scale”) is what the blues is all about.
The melody itself is odd. The verse starts on an unstable 4th (just like Day Tripper) and rocks back and forth between the 4th and the equally unstable b3rd. That's D and C natural repeated over an A major chord which contains C#.
The Chorus itself is the least catchy part of the track, overly syncopated and rushed, perhaps to accent the play on words (is it “I'm backing the USSR”?) but using the same turnaround on the chorus (0:30) and bridge (1:08) and dropping out to accent the key lyric on the last line of the chorus are nice touches (see Tickets 41 and 30).
Next up: Wild Honey Pie