Also from the link..
But given the tone and tenor of LBJ's conversations on these issues, I think the best we can say is that the quote cited by OP is not inconsistent with LBJ's style. But it seems unlikely that we will ever know if those exact words were uttered.
From my own studies, I personally think the quote is either genuine or a fair paraphrase. It's the kind of thing LBJ might say to a Dixiecrat to convince them not to oppose the CRA. Thus, if anyone got "tricked" over the CRA, it wasn't black America -- it was Southern conservative democrats. In other words, as
u/Thurgood_Marshall and others note below, while the quote might be genuine, the sentiment was not.