"Are you saying the body of Christ is the body of, I dunno, Joe down the street?"
Enough of the sarcasm. Read St. Paul who speaks of all Christians as members of Christ.
The body of Christ is the Church, which is comprised of its members universal (catholic). The "catholic" church of antiquity was united under the Bishop of Rome. The properization of the word "catholic" (to capital "C") was not a result of filing articles of incorporation down at the Roman Chamber of Commerce. It was that which most completely described the body of Christ - the church - universal - Catholic.