The relevant definition of operation in Merriam-Webster's Eleventh Collegiate Dictionary (2003) doesn't mention cutting as a prerequisite:
operation n ... 4 : a procedure performed on a living body usu. with instruments esp. for the repair of damage or the restoration of health
Under the Eleventh Collegiate's definition, a bone marrow transplant would certainly be an operation; in fact, it might be viewed as two operations—one on the donor and one on the recipient. Any more-precise notion of the meaning of operation as a medical term of art involves a more sophisticated understanding of the term than Merriam-Webster seems to possess, and I think it is asking a lot of an eleven-year-old to be expected to possess it.
This is not to say that the operation in question may not also be characterized as a procedure.