Counterfactual reasoning: A logical fallacy?

You must have heard the counterfactual argument a thousand times: if the program had not occurred, the effect would not have occurred as well.  Let us dissect the logical form of the argument.

In symbolic logic, the counterfactual argument has this structure:
If Program X is implemented, then Y happens (X ⊃ Y)
Program X is not implemented (~X)
Therefore, Y does not happen. (∴ ~Y)

This reasoning is fallacious.  It has even a name which is denying the antecedent.   Michael Scriven calls this overdetermination in his debate with Tom Cook.  This is a logical fallacy because even if X is false (~X), Y can be true (~~Y).  As can be seen in the truth table below, a false antecedent (X) always yields a true logical relationship (X ⊃ Y) regardless of the value of the consequent (Y).

Truth Table

X	Y	X ⊃ Y
T	T	T
T	F	F
F	T	T
F	F	T

Why is this so? Because in real world, it is not only Program X that produces Y.  Other programs or causes can produce similar result. Suppose a donor claimed that because of the financial assistance to farmers, the household income of program beneficiaries increased.  This reasoning failed to consider that the household income will increase even without the financial assistance because of other contributing factors such as improving economy, better weather conditions, other donors, etc.