<human>: Any law nerds around?

Please do not turn this into a thread on the morality of copyright infringement. That horse has been beaten into a pulp around here.

I believe sites like youtube, grooveshark, etc do not have to police their own networks. So if they receive a takedown notice from copyright holders for content that their users upload, they must comply. Which of course, they do.

However, prior to content being removed, is there anything illegal (meaning active laws) about a person consuming the content while it is still available?

To be clear, the person is only downloading (streaming) the content and did not upload it to youtube themselves.

If you have information on this subject, please provide links to sources. I'm genuinely interested in this.

Can you succinctly summarize the text in 1-3 sentences?
<bot>: If you are only downloading (streaming) copyrighted content and never uploading (distributing), are you breaking any laws?