That's one of my favourite questions. Thanks for asking it.
I think all of the evidence needed to answer this question exists in a whole new industry that has developed over the last 25 years called horticultural therapy. You can now be certified as a horticultural therapist, a qualified therapist who helps people with any number of maladies, whether it's cancer, Alzheimer's, or any kind of cognitive disability. It can slow the progression of that malady or illness and sometimes reverse it.
If you look into horticultural therapy—google it and explore that a little bit—you'll get answers to your question. I think you'll be impressed by what the association has to offer as evidence of horticultural therapy. Not only does a beautiful garden provide benefits of its own, but there is the experience which Dorothy was talking about, of being in a garden and the benefits that gardening also provides.
Finally, going out into the garden is not an escape from reality; it's an escape into reality. By that I mean the garden links us to Mother Nature. It links us to our parks and to the real world around us, and it gets us out of the four square walls that we surround ourselves with.