"In the same vein, it's fair to say that members of today's "coalition" are allies, in that they've taken a stand in support of the US. What's lacking is their formal and direct participation, and they's why it's false to call this group today a "coalition"."

The definition of coalition does not have a strong association with conducting a war. It certainly is not exclusively used to describe two or more nations conducting a join miltary action. An alliance means "a close association of nation or other groups, formed to advance common interests". Again, not exclusively talking about nations forming up into one army.
Therefore for example, it could be said that there is a coalition fighting Terrorism. Or a coalition of against drunk drivers. Or a coalition against teenage pregnancy.

'The precise choice of words conveys a precise meaning that conditions how people think and how they act on their thoughts. "In the beginning was The Word"...'

Indeed.

{Whenever you find yourself agreeing with a dog, you should do a reality check:}