I find the concept of parapolitics "a system or practice of politics in which accountability is consciously diminished" useful for understanding something like this. Study this article carefully, and here is what you see:
a) The source of the rumour is British.
b) The British prime minister has expressed a view that coincides with the view of the potential resignees.
c) A Pentagon source appears to have been selectively quoted; his or her views could easily be contrary to the rumour.
One could easily conclude that this is a British signal to the Bush administration to lay off Iran, that the British cannot be counted on to support an attack. It could even be a call by the British to anyone in the American military with misgivings about an attack on Iran to look to them for help.
Articles like this always make me suspicious of neatly packaged historical descriptions. Real life is a lot more messy.