No, not a lack of copyright but basically, I can't be charged for possessing information, such as I can't be charged for having BrittneySpears.mp3 or SuperMarioMegaROM.smc on my computer. Downloading things might be still considered a civil matter though, but after you downloaded them you are free.
So... It's only illegal if you get caught in the act? We don't expect this to cause issues? I didn't monitor you downloading the mp3, but you have on your computer a file identical to three thousand others, and not a Britney CD in your ownership? Are you arguing this does not fall under the definiton of "stolen property"? All arguments about imaginary property aside, of course.
Twitter's not just bad for this - oh my, a new form of spam, I never saw it coming - but for poor context community as well. I feed my Tweets to my blog in a widget (Geekiest phrase ever, I know) and, thus, am searchable. Now, I put up a "Legal" page about my site - claiming authorship and all - and immediately was added by nearly forty Law-oriented "Free Advice" Twits who likely had never read another of my posts. I changed the page's name from "Legal" to "Disclaimer" and the additions halted. Changing the page to "Copyright" had the same effect - media trolls, dozens of them, now on my block list. It's incredible.
Twitter's nice for micro-posting, but seriously. This shilling thing? Been going on for some time. It's nothing new.