Can meditation heal physical diseases?
In case it matters, another translation says,


  "If you were to recite to the mendicant Girimānanda these ten perceptions, it’s possible that after hearing them his illness will die down on the spot."


I think everyone translates the Pali, "Ṭhānaṃ kho panetaṃ", as "It is possible that".

Also, though this doesn't answer your question, Piya Tan has an introduction to this sutta if you want to read it -- Giri-m-ananda Sutta (A 10.60) -- which includes a page connecting ancient Indian medicine with early Buddhism (and explaining the ten perceptions in more detail).