Normally journals claim copyright on the published version of the paper, after it's been edited and typeset by the journal, and don't mind academics sharing the original "preprint" version that was edited and typeset by the original author. (They don't have any reasonable copyright claim on the preprints anyway.) Sending takedowns on preprints is unusual enough to make the news, which is why it's on Slashdot now.
The journal also doesn't pay the academics for their papers; journals work like distributors in the retail market, i.e. their purpose is to make the papers more widely available / discoverable / searchable, in addition to reviewing them to ensure appropriateness and quality (although it's arguable that this is actually a useful function of the journal, given that they don't pay the reviewers either).
Incidentally, my papers have been published in multiple conference proceedings, and I didn't sign a contract for any of them. I assume the contract exists, but the papers were all coauthored, and I think the journals only sought a contract with one of the authors. If this is indeed the case, it makes the situation even more complex.