Dr. King's most famous literary work is his Letter from a Birmingham Jail, written while he was imprisoned after a protest in April 1963. In it, he criticizes fellow clergy who supported civil rights, but wanted to wait until it could be accomplished without civil disobedience or widespread unrest.
...When I was suddenly catapulted into the leadership of the bus protest in Montgomery, Alabama, a few years ago, I felt we would be supported by the white church. I felt that the white ministers, priests and rabbis of the South would be among our strongest allies. Instead, some have been outright opponents, refusing to understand the freedom movement and misrepresenting its leaders; all too many others have been more cautious than courageous and have remained silent behind the anesthetizing security of stained glass windows...
In both your quote and in the Letter, King is expressing the idea that it doesn't surprise us when our enemies lash out at us. That's naturally what an enemy will do. However, it is a shocking betrayal when a "friend" is not even willing to speak up to defend you.