Translation:This patient does not need help, he is already healthy.
I have the same complaint as with the other sentence that uses "already healthy" -- it's really not a thing that's said in English when a person was sick or injured a short time ago.
In that case, people tend to highlight the improvement: "already better", "recovering", "recovered".
Could you accept those?
I believe that there are other sentences where any is accepted, even though there is no żaden in the Polish sentence. It seems to me that there is no exact equivalent to any, since żaden is stronger, thus closer to any... whatsoever. I would be in favour of accepting it here.