Honestly, it doesn't seem like the foam roller can produce the benefits of releasing trigger points like the hands on approach does. Localized areas of "knotted" tissue require other means.
However, I do see one glaring benefit to foam rolling. The best athletes in the world are usually parasympathetic dominant, while most others can't seem to get back into a parasympathetic state to recover fully; hence one of the many reasons elite athletes can do more work per session more often. Foam rolling acts as a superficial massage technique which is related to activating the parasympathetic system. Additionally, research shows the body begins releasing catecholamines PRIOR to the beginning of exercise to stimulate your sympathetic system in anticipation of training.
So, to me at least, this says foam rolling before training could essentially be counter-productive in terms of stimulating the body to train and that foam rolling post-training could act as a tool to return to a parasympathetic state and begin recovering quicker and more efficiently.