Then it is unproven that LBJ said those words. Which is why I asked the question of proof that he did.First, sorry for the delay in responding, I've been out of town. Second, the answer to your question is "depending on how you define hearsay, no, I don't have unquestionable proof."
If you look at the Snopes documentation of the statement it is listed as unproven. It's initial sourcing is Ronald MacMillan, an Air Force One steward who acted as a eye witness source in the 1995 book, "Inside the White House" by Ronald Kessler. Some people have questioned whether or not MacMillan is telling the truth. Among other anecdotes in the book was Linda Baines Johnson allegedly tellling MacMillan "Go find my N@gger." She denies ever having done this, but then, she naturally would make such a denial whether she had done so or not. So much depends on whether you trust MacMillan's statements and find him credible -- as an eyewitness, and if you find him credible, his statement would not be hearsay.
LBJ was a notable "man of his time" quite comfortable in using the "n-word" and his motivation for passing the Civil Rights Act of 1964 has often been questioned. At least according to MacMillan by way of Kessler, his motivation was straightfoward partisanship, "I'll have those n@ggers voting Democrat for 200 years." While the statement may or may not have been made depending, as above, on MacMillan's veracity, it does explain a possible motive.