I've heard from plenty of people that it worked for them, and it makes sense to me: some plants are extremely good at getting their roots down deep and they can do the same work that a tool would do.
That said, here in Georgia I have extremely dense clay soil under a thin layer of topsoil, and nothing I've tried (even daikon) is able to penetrate it. I figured that maybe I was doing it wrong, but David the Good posted a video of a friend of his in Georgia who was having the same issue. Sure enough, she had my recognizably dense, orange clay, and she showed how daikon would just kind of sit on top and wither rather than punching down. She ended up having to use a broadfork to break up just enough of the clay to get moving.
So I think the answer here is that there are a number of plants that can break up compacted soil, but you can definitely have levels of soil compaction that are beyond their capabilities. Someday I am going to try the method (which I think is Paul's) where you dig, like, six-foot holes at regular intervals throughout your space and fill them with organic matter. This allows the remaining, compacted soil to expand naturally into the gaps you've provided, while being enriched by the organic matter and the worms, etc. it attracts. The obstacle, of course, is that you have to dig a lot of really deep holes in really hard ground.
