I heard that story, or something similar, years ago, and had forgotten about it. I don't remember the "pigs" remark, but I did remember that the extra security had been declined. Wonder how the person who made the decision felt about it afterwards.
Extra security might have made a difference and perhaps not. Kennedy had the image of a populist and insisted on pressing flesh.
I think had he been elected he would not have begun an immediate U.S. withdrawal from Vietnam as was advocated by McCarthy and later by McGovern. I think Kennedy would have gone for a phased withdrawl like Nixon accomplished.
Despite all the historical revision, Bobby had a hand in the plots against Castro:
http://www.findarticles.com/p/articles/mi_m1316/is_n12_v27/ai_17828366