Once more with feeling: Yes, the chiropractor needs the radiologist's report, because the chiropractor is not a radiologist. A radiologist is a real doctor who has done a five year residency in radiology, and who is required to take continuing education credits to maintain certification.
You have the disc to take with you to any specialists that you might go see. It's standard procedure - when you go to see an orthopedist or neurosurgeon, they'll ask you to bring the disc with your MRI.