The claim of "Iran funding terrorism" is in fact due to its recent (as in decades) support of Sunni Hammas, which is the most direct threat to Israel, and which started as a Muslim Brotherhood offshoot financed also by the Saudis.
Fascinatingly, Islamic Hammas was also once seen by Israel as the "potentially better" than less religious PLO and Israel even indirectly supported it, almost like the "moderate" Islamic rebels are still supported by the US.
http://www.wsj.com/articles/SB123275572295011847
Time and again it turns out that every "Islamic" group will eventually turn against the West. Those that support them don't understand the basic tenets of the religion behind.
