Who is conning whom?

The Church of England wants to clamp down on sham marriages. This morning the Bishop of Ripon and Leeds told BBC Radio 4's Today that vicars are being conned.
He did not say that the Church had opposed Mrs. Thatcher's 1979 election policy to end the concession whereby foreign men can live and work in the UK through marriage.
If they couldn't do that they wouldn't look for someone to marry in order to stay here.