If I were in LBJ's shoes I'm not sure I would have done anything about it, either. Not that the Cuban involvement is necessarily a good thing, but when you look at it objectively it was really just a matter of fair play. Kennedy tried to have Casto killed, and Castro tried to have Kennedy killed. So Castro was successful . . . big deal. No reason to get the whole country involved in this kind of nonsense.
If this sounds harsh, just realize that one of the most disgraceful aspects of the Kennedy administration was the manner in which assassinations -- attempted (Castro) and successful (Diem) -- of foreign heads of state became an acceptable means of pursuing our foreign policy objectives.