Break the principle into its two required ingredients. First, the intoxication must have left the person incapable of understanding the nature of the act. Second, and separately, that intoxication must have come about without the person's knowledge or against their will. Both ingredients need to be present for the offence to be excused.
On these facts, B and C were persuaded to drink, but persuasion is not the same as being intoxicated without knowledge or against one's will, both men knew alcohol was being poured and chose to keep consuming it after being talked into it. That failure on the second ingredient is enough to keep the exception from applying at all, regardless of how the first ingredient might have played out.
With the exception unavailable, ordinary liability rules apply, and it is C, not A, who committed the actual pushing that injured B. A's persuasion explains why the drinking happened, but it is not the act that caused the injury, so liability for that specific act rests with C alone.
So the correct answer is C is liable.
Asking what fact would need to change for each option to be correct isolates the real issue quickly.
Since the drinking was voluntary and the pushing was done by C alone, the option that keeps liability on C is the one that needs no unstated fact to be true.
Therefore, the correct answer is C is liable.