"the Church is His Body and that Body may sin"

     "Not long ago Mr Middleton Murry wrote a book in which he spoke of 'the betrayal of Christ by the Churches'.  To this Father Gerald Vann wrote a reply in which he spoke of 'the betrayal of the Church by the Christians'.  Both were concerned with the same facts, but Mr Murry spoke as a Protestant, Father Vann as a Catholic.  It is impossible for Christ to be betrayed by the Church, because the Church is His Body and that Body may sin and so betray both Christ and the Church, and this is the situation in which we find ourselves.  We are all more or less guilty. . . ."

     Bede Griffiths, The golden string, chap. 10 (Catholicism) ((New York:  P. J. Kenedy and Sons, 1954), 158).  I get the distinction, but isn't this poorly formulated?  "It is impossible for Christ to be betrayed by the Church," which "is His Body and . . . may sin"?
     I was referred to The golden string by C. S. Lewis in Surprised by joy, but found it inferior.  Absolutely everything as a major turning point.  An excessively Whig memoir.