Even if there was, it certainly wouldn't define culture solely as "Hollywood movies and pop music". Broaden your cultural horizons.
Just like if you were to say "access to clean drinking water is my right", that wouldn't entitle you access to ALL clean drinking water. Just like "access to culture" wouldn't entitle you to pirating whatever content you feel like.
If you're going to try and take the moral high ground, do it right and just avoid consuming content produced by organizations you disapprove of.
A much stronger pro-piracy argument in my opinion is that of convenience and consumer experience. Legitimate paying customers suffer under the tyranny of DRM while pirates have a much better experience. If I buy a song on the Apple music store I may not be able to play it on every music player[0]. If I pirate it then I can convert the format and consume it however I like. Video games with DRM may require an Internet connection to "validate" when the pirated versions are available offline (remember that Sim City debacle?). What's worse, remember the SONY rootkit disaster? Also, Ubisoft actually had a remote code execution back door exploit for a while. I've never heard of a DRM that made anything better for the paying customer.
[0] This has apparently changed in recent years.