To me it has meant that we all killed the Kennedys by our acceptance of the way things were in America at that time. That we couldn't sit on the sidelines and blame the government or some crazed lone assasin for these killings. It seemed to be a cry for us to rise up and revolt against the government.
This was a time of a huge amount of tension in the U.S. partly due to the Civil Rights movement, coupled with the anti Vietnam War protests. My brothers were about 8-10 years older than me at that time, and they were of the Beach Boys, everythings all right if you're white era. I was in a totally different environment where we were pretty much revolting against everything that our parents stood for. And to see our heros assasinated caused a lot of despair, hate, anger, disillusionment, "blaming", as the song asks about, and general confusion about our country and its future.
A movie that really struck home to me that played in the theatres recently is, "Across the Universe". In it is the assasination not of one of the Kennedys, but of M.L. King. However, the reactions to these killings was the same, one of wonderment as to who on earth would want to see these heros dead?!!! So, the question, "Who killed the Kennedys?" came a lot just from shock. But I guess it also is actually asking literallly, "Who"?
I hope this helps.