Of course it makes sense: neither the US nor the Iranians want to get into a shooting war over Bahrain. So they have both decided to agree that each will keep their hand out of the political situation.
In the case of Syria, then Israel could get involved. Israel has annexed the Golan Heights area and declared the people living in that area who refuse to accept that they now live in Israel to be of "undefined nationality". Syria does not recognize the annexation, but tolerates it in the sense that it does not shoot at Israel to get it back.
A shooting war in either such a sensitive place would be disastrous for all concerned. It could stop the flow of oil and cause serious and long lasting unrest.
I doubt that the CIA could have enough assets in Syria or Bahrain to make any appreciable difference.
In Bahrain, the Shiites are treated unequally, and Iran dislikes this. The US has a policy that all citizens of all countries be treated equally: it is in the UN Charter. But the US values good relations with the Saudis more than it values civil rights of a relatively small number of Bahraini Shiites. In other words, we are on the wrong side of the issue morally, but economically we are on the right side, so we have agreed to do nothing and let the locals work it out.
I imagine that there is a secret agreement regarding what we will and will not tolerate in Bahrain, and another regarding what we will tolerate and not tolerate in the Golan, and the Saudi, Bahraini and Syrian governments all agree on this.