The original sentence is not wrong.
And the definite article certainly means what you want it to signify: [among] all the decisions that governments face I am specifically referring to the one that regards this specific issue. Logically, then, you would use the.
Here is an example:
Each government faces the decision whether to dollarize or not.
Just google the web for "government faces the decision". Make sure to include the quotation marks. Then show all those examples to whoever told you to make that "correction". :)
And again, I prefer the first sentence. That is, I prefer the definite article here simply because it is definite. It is kind of equivalant to 'that decision that everyone knows must be made'.
By contrast, the indefinite article weakens the importance of 'the' decision.
A decision is like saying 'any decision' or 'any old decision.' It doesn't matter what decision the government makes as long as they make a decision. And that to me weakens the statement and the importance of the decision.
This is a simplification. But there is a definite difference in meaning between the and a and if you want a stronger sentence, because you want to talk about the decision that everybody knows has to be made, use the.
Articles are tough to get hold of, and their use is extremely difficult to explain. But you seem to have a good grasp of what you want to say and why you want to use the definite article, and I support that usage.