A lot of the Middle Eastern countries may not actively support terrorism, but they most certainly turn a blind eye to the militant groups as they operate, plot, gather resources and move people from country to country.
These countries, as Saudi Arabia learned the hard way, are inevitably targeted by the militant groups they are host to. They assume that the militants only target western countries... what they fail to realize is that the objective of these groups, which is to establish a single world-wide Islamic state, requires ALL countries to be overthrown... including themselves.
As the middle astern countries start to feel the sting of these groups, they will most certainly shut them down? as Pakistan and Saudi Arabia have been doing.
There is absolutely NO WAY a significantly organized militant group can operate within a given country without the knowledge of the authorities. The logistics alone will draw the attention of the private sector... food, clothing, housing, weapons, transportation, etc... all of those things are blatantly visible to anyone in the community. It would be like no one being aware of the Branch Dravidians compound until the ATF moved it... hell no! Everyone in that area knew what was going on in that building. The local gun shop knew them as one of their major clients.
It's the same as everyone on a street denying knowledge of a crack house on their block despite all the traffic in and out of the house all day and all night.
You just can't hide organized activities. People always notice.