The Beatles are classical music. When visiting a few music CD shops worldwide, I saw them classified under "Classical". Admittedly, these shops had no (or very little) music older than the Beatles'.

Quotations of earlier music or use of earlier styles had always occurred and will always be occurring, because this is what music is about. Some musicians like to give sometimes a touch of "old" in order to sound interesting or to prove that they know their classics. That happens in any type of music.