Add to that mix tribal allegiances, the cross pollination of all groups seeking their own agendas and you have the situation where some very wealthy religious extremists can fund their agendas worldwide including "terrorism".
Too many posts are seeing everything as black and white. The Saudis from the top down planned 9-11 etc.
Just like in the US, there are hidden agendas, secretive groups akin to the CIA all pushing their own agendas whether financial / religious. And just like some in US politics, there are some pushing for the end of days where their chosen deity / son of / prophet of returns and leads them to paradise / the next world.
So on the one hand it's true that Saudi Arabia and a government funds terrorists and extremists, but that's not at all their intention and as has been pointed out many of these organizations would quite happily slaughter the Saudi royal family.
The again, there are some individuals within the regime and probably at some levels within the royal family itself, that actually do support terrorists and extremists.
It's a real mess.
That's a very charitable view, especially for a monarchy that exerts tight control over many aspects of life in their country. That is not insisting on simplicity. Pakistan's government, and their security services, for example, are manifestly capable of working multiple conflicting agendas. But that doesn't mean they can be excused.
As others on this discussion have pointed out, Saudi has exported both terrorism and the fundamentalism that gives the terrorist fishes a much larger sea to swim in. The US, in part because if its own problems with religious fundamentalism, is unable to forthrightly work against religious fundamentalism and other excesses in religiosity, such as suppression of women's rights, in the Moslem world when that might be the most effective way to reduce terrorist incidents. Imagine trying to end the Soviet Empire without detente.
So, yes, that is a real mess.
I think you may be right (I haven't enough information about Saudi Arabians or their views to tell) but I really want to believe that the real-life politics is much more rational than in a game of Civilization.
However, it is completely rational: "spreading democracy" is valid not only from idealism, but from the notion that it's much easier to deal with governments and societies that share your values. Of course, US have not always followed this motivation throughout history, but in case of islamic arab countries in the last years, US has pretty solod record in that regard.