Hey, Wikipedia says Foo Fighters are alternative rock, so therefore they must be. Then again, going by that same logic, the Red Hot Chili Peppers are also an alternative rock band.
Does that matter? No. Alternative rock is (you guessed it) still within that genre called ROCK!!!
When the alt-rock genre started being discussed, various well-established rock artists, including U2, REM, and Elvis Costello. RHCP were included too, as well as many sub-genres. Similar to 'classic rock' the genre was largely defined by innovative radio stations, such as Atlanta's 99x.