Maybe not as much when compared to piracy of new releases, but
very little? That's simply not true.
How do you explain the majority of modern independent music being heavily inspired by 80s pop and 90s hip-hop, especially when most of the producers are too young to have remembered listening to it over the air? What do you say when you look up an old music video on Youtube, and 70% of the time, the top comment is from a teenager? "Today's music sucks I'm 12 and none of the kids in my class listen to this but I think it's awesome like this if you're watching this in 2012!!!" has even become something of a cliche or a running joke at this point.
How do you explain What.cd, probably the largest private torrent tracker in existence, being largely dedicated to preserving and distributing out of print music? Anyone can find the latest Skrillex album on The Pirate Bay, but the true music lovers come to sites like What.cd to discover and trace the lineage of what they'll never hear on the radio.
How do you explain the ROM piracy scene, loved both by nostalgic 30-somethings and kids who never owned a Nintendo? How do you explain the people that spend months or even years painstakingly reverse engineering old, obscure games and translating tens or hundreds of thousands of lines of text, just to give them the treatment they wish had been available to them on a store shelf as children? What about the ones that do it completely anonymously, never receiving real credit for their contributions to history, in fear of legal repercussions or being socially stigmatized based on the subject matter of the works they translate?
Ditto for the anime/manga scene, where there is a seemingly endless supply of interesting old works in need of a translation?
How do you explain the continued love for classic films, from everything Disney's put out, to the original Star Wars trilogy, to Blade Runner, and so on?
There is a lot of cultural value in media that isn't exactly fresh. Private collections have allowed us to preserve the physical artifacts of human creation over the centuries, but a manuscript sealed in the tomb of a museum quickly fades from the public consciousness. The magic of internet-enabled piracy is that it has allowed us to keep mankind's creations culturally significant long past their expiration date, on an unprecedented scale. Today, we don't just remember the most standout works from previous decades that our parents passed down to us (or the ones their parents passed down to them). We discover things that few cared about when they were actually created, and give them a new life that their creators could never have predicted.
I suppose it may be hard to understand if you aren't in the thick of it, but so much of our modern culture is about appreciating and drawing inspiration from the past that an assertion like there's very little pirating of content that is over 20 years old completely baffles me.