All Aaron Swartz did was jack into an Ethernet port in a closet that was unlocked in an MIT building, and get an IP address from an unsecured network at MIT, and then wrote some Python scripts to work as a web robot and pull down articles. The web robot did the same thing as any user at MIT could do, read and download papers.
So yes it is possible to allow free, unrestricted access, JSTOR just decides to only do that to certain IP ranges. If they allowed that with everyone, Aaron wouldn't have to jack his laptop into an unused open closet to pull articles.
In fact there was no real crime committed, other than trespassing at MIT, and MIT didn't press any charges to that effect.