IIRC modern terrorism is generally thought to begin with the anarchist assassinations of the late nineteenth century. Anarchists murdered Tsar Alexander II of Russia, Empress Elizabeth of Austria, King Umberto of Italy, President Carnot of France and US President MacKinley amongst others. There were also some particularly brutal terrorist groups operating in the early decades of the last century, especially in the Balkans. I believe VMRO (Internal Macedonian Revolutionary Organization - which confusingly split into two: an "internal" and "external" faction) still holds the record as Europe's most violent terror group.
I'm familiar with the Russian terrorists of the 19th Century and some of the Balkan groups. I think I picked Sarajevo in 1914 because of the perception that the short, twentieth century began in 1914 and ended in 1989. I suppose it depends on what one's definition of modernity is. Starting with the Jews in the Palestine Mandate seems to me, though, to be a less defensible proposition for the beginnings of "modern" terror.
Having recently re-read parts of Albert Camus' book "L'Homme Révolté" ("The Rebel") I think the "morality" of modern terrorism was developed by those Russian figures (and, of course, in books like "Reflections on Violence" by Georges Sorel, a particular favourite with both extreme leftists and rightists from 1908). I think there is a continuity between their thinking (and actions) and that of contemporary fanatics. Incidentally, I believe there was an international conference held in 1937 by the League of Nations to agree on a generally acceptable definition of the concept "terrorism", but the conclusions of the conference were never ratified due to the outbreak of World War Two.
After having read your post and the comments, I don't know why they chose the Israeli example as the first modern terrorist action. I have to confess I missed the first three shows, and so this was more of a summary at the end that I got.
In a promo blub, it says: "The first part, In The Name Of Liberation, looks at the use of terror by national liberation movements around the world, starting with the bombing of the King David Hotel in Jerusalem by members of Menachem Begin's Irgun terrorist group in 1946"
But that still doesn't explain why it picked that particular moment as the beginning of modern terrorism - maybe because of the link btwn the use of terror and political liberation movements? I must confess I am not well versed enough in modern terrorism history to be able to make an informed comment.