For most of its history, the band chose to stay away from the political realm. However, in 2004, upon learning that George W. Bush's presidential campaign was using "Times Like These" at rallies, Grohl decided to lend his public support to John Kerry's campaign. Grohl attended several Kerry rallies and occasionally performed solo acoustic sets. The entire band eventually joined Grohl for a performance in Arizona coinciding with one of the presidential debates.
I have a theory that it's impossible to prove anything, but I can't prove it.