The story about the coup appeared in a Saudi newspaper at a time when relations between Saudi and Qatar were at a low point - the Saudis are not happy with the fact that Qatar is attracting so much attention. Also, since 1995 when the present Emir deposed his father in a (bloodless) coup contacts between the two countries have been strained, when you add the freespeaking Al Jazira TV into the equation as well you will understand that neighbourhood relations are not what they could be.
I live in Qatar and no-one I know (military, diplomatic, local community etc) was aware of a coup. Maybe you will accuse me of being naive but I assure you my sources are more reliable than the local press or the internet. The story is in a similar vein to the one that the Foreign Minister went to Israel to meet politicians last summer - i.e. an attempt to discredit the Qatari government in the eyes of the Arabic world.
Give the Qataris some credit for using the Americans as their insurance policy against their bigger and very jealous neighbour casting envious eyes over the huge gas reserves that exist here.
And yes, expats do feel safe in Qatar.