London's folk rock band Treetop Flyers derives its name from a U.S. helicopter platoon known for flying low-altitude missions during the Vietnam War (and not from Stephen Stills' track Treetop Flyer). The band's affinity for things old and American also extends to its May 2011 single Things Will Change, which borrows heavily from the U.S. folk rockers America and their 1972 hit Ventura Highway (e.g. G maj7 to D maj7 chord progression, vocal harmonies). Check it out.
While the melody in Avril's tune Here's To Never Growing Up (starting around :14) seems similar to the melody in Oath (starting around :35), it's also reminiscient of Avril's own hit Complicated, which predates both songs. In other words, the melody in Here's To Never Growing Up (Avril) seems similar to the melody in Oath (Cher), which seems similar to the melody in Complicated (Avril)!
For me the similarity is mostly in the vocal lines, where Billy sings "Oh oh oh oh" (around 2:40), and Pink on the choruses sings "Ah ah ah ah, sun is blinding" (around 0:26), as well as the production value (i.e. the heavily reverbed snare), vocal lines doubled an octave apart (a la Righteous Brothers and a million Motown/Philly Soul records).