They do own the right to the composition of their collection, so someone who got the whole collection would be liable to infringing their right on the composition of the collection; in contrast, a random sample of articles would infringe on the publishers' IP rights rather than J-STOR's.
The subtle point is that J-STOR is absolutely not interested in the original copyright owners having to hunt down abusers, because that would (in all likelihood) appear like an additional, avoidable hassle to the latter and would make them less likely to agree to have J-STOR distribute their content. [edit: apparently it's the US Attorney General more than J-STOR who is pushing this case forward]
In comparison: if someone sneaks into a cinema to see a movie, you would accuse him of cheating them of the entrance fee, and not of "stealing the movie". If someone sneaks into a cinema and uses his camcorder to record the movie, he is cheating the movie theater of the entrance fee and misappropriating the production company's movie (with the suspicion that he might pirate it later), but he did not steal the movie from the theater. That would involve something like walking away with the movie theater's copy of the movie, which would fulfill the criterion that what's stolen is not there afterwards.
Misappropriation of IP is not stealing. It's unauthorized copying - that certainly has the potential to harm the bottomline of the copyright owner, but with an impact that is much harder to quantify than the stealing of an actual physical thing.
IP owners and friends of them who use the word 'stealing' want to frame the situation in such a way that appeal to the nonexistence of monetary loss is excluded - mostly because these same owners are investors in, and not creators of, the IP and do not have any other perspective than squeezing whatever value they can out of their investment.
(The authors of the original articles probably couldn't care less about some punk illegally downloading their texts, because they don't see any money from it anyways).