The problem with making a big deal of the LBJ quote, is that blacks had already permanently switched parties after the 1932 election.
Northern Blacks moved Democrat after 1932, but were not voting overwhelming en bloc (for example, when Republican Oscar DePriest lost reelection to his IL Congressional seat in 1934, the Black Democrat who beat him still received only a minority of the Black vote and was elected by an overwhelming majority of urban Whites in that district).
Most Southern Blacks were disenfranchised and would remain Republican until the 1960s.