The KGB was trying to sponsor the Civil Rights movement to weaken the US. What I mean by it being a lie even when it is true is that the statement implies that the movement is fabricated or unworthy by their support. It is a distraction.

In reality the merit of groups exist completely independent of who sponsors it and even giving money is no guarantee of control. Even if the KGB gave millions to Martin Luther King that wouldn't make fighting segregation the wrong thing to do suddenly any more than accepting Soviet funding of a smallpox vaccination means that eradicating smallpox is suddenly wrong.

It is especially bad since it is used to discredit /the movement/ itself as opposed to any actor being questionable. Martin Luther King cheating on his wife didn't make the civil rights movement wrong.