My two cents (which is all it's worth) . . .
I'm a big guy -- I started triathlons a few years to lose weight -- and running has always been difficult for me because of joint pain from my weight and lack of running experience. I convinced myself that I could train for the running with long sessions of the elliptical trainer I have at home. It didn't really work. In my triathlons, on the run, while my lungs were fine, my joints were killing me. My knees and ankles hurt so bad I could hardly walk.
I put up some Internet posts on forums like this explaining my dilemma, and asking about training for running by not running, and I got roundly mocked. Eventually I started running on a treadmill, just a minute or two longer each time. And slowly I built up some tolerance. Now I can run without pain. I'm still not fast, but no pain.
So, in my limited personal experience, while the eliptical trainer increased my cardivascular fitness, it didn't get me where I needed to be. Although I undertsand that world-class runners and triathletes don't go around pounding their shins into the ground for "training," that is probably because they run all the time anyway. I think there is some merit to the idea that beginners -- whether beginning in earnest, or beginning back from a hiatus or an injury (or, more specifically, beginners who are fat guys like me) -- might have to build up a fundamental level of tolerance in the joints through some level of pounding that comes from actual running.
None of which is to say that I would recommend pounding on a recently-injured joint, but I'm no doctor (or runner).