The meaning of the line "The fault, dear Brutus, is not in our stars, but in ourselves, that we are underlings.' is that we can't blame "The stars" or "destiny"; we must blame ourselves because our decisions are what plans our life's route. Weather it's good or bad, bumpy or smooth it's all based off our decisions. So in blaming the stars we are running away from the reality that we did something wrong. But we can't blame the stars because of something we did for it blame the stars is to blame the kids for their parents doing wrong, it just doesn't work. But as we are "underlings" or "humans" we make mistakes, where as, "the stars" are "Holy" or "higher than us" and they know how not to make mistakes.
I think John changed the words in the quote because it changes the meaning of the quote, to what I think is, The main theme. "The Fault in Our Stars" means that "Our Stars" have changes our route with out our approval. The straight and smooth route that we had planed for ourselves has been changed by "Our Stars" to have bumps and detours that are never ending. Hazel did not plan to get cancer but her stars did. So her smooth route with high school then college then a job and a family was sent in a different direction completely. Now its changes to just making it though the day. (Since you know her "lungs suck at being lungs") So the title is "The fault in Our Stars" because it's saying that thou we can't blame the stars fro our mistakes the stars can still ruin our plans by adding their own "mistakes" or "hardships."