Yes it's true. Rock and Roll music (and essentially every music out there), can be traced back into country western roots. If you think about it, what did people have to listen to back in the early days? Country and Blues. Blues music came popular later on into the 20th century with the African American community. But Country had been around for such a long time before then. Country music was the driving force behind blues music, which in turn was the driving force behind classic rock (60's and 70s music). Which is the driving force behind the majority of todays music. I remember watching an interview with Jimmy Page showing his collection of records from the 1950's and back. He listened to artists like Muddy Waters, John Lee Hooker, and so forth. Toni Iommi listened to the same people, and so did Angus Young. (For those who don't know who these men are, they are the guitarists of Led Zeppelin, Black Sabbath, and ACDC). The list can go on from artists of back in that genre of their influences. But artists of today generally listen to artists such as Zeppelin. So Zeppelin has influenced Green Day. Not only does Green Day take Zeppelin as their influence, but they take all of Zeppelins influence as well. Which is the old blues guys, who were influenced by the old school country guys.
So to sum up, everything and anything that you'd listen to today, has some form of subtle country influence involved in it. You may not hear a banjo pounding away on the track, but the chord progressions of the guitar, or the drum beat may have been stolen from a once very popular Johnny Cash song.