If the effects of an event card are canceled, the card is still considered to have been played, and it is still placed in its owner’s discard pile. So if I cancel my opponent's Seen in Flames with Hand's Judgment, he is still considered to have played the Seen in Flames, and he can trigger Melisandre's reaction to playing a R'hllor card. Furthermore, when an effect is cancelled, the costs remain paid (gold is spent, characters are knelt, etc).
The printed value is always the value that is physically printed on the card - regardless of any modifiers (RR p16, "Printed"). In the case of a card with cost "X", the printed cost is the letter X - regardless of what the actual cost paid was. The letter X has its own entry (RR p.23) which clarifies that when not specified by a card ability or player choice, the letter X is treated by the game as 0 (rather than, for instance, "null"). Since player choice or card ability cannot influence the "printed" value, the rules tell us that the printed value of X is equal to 0.
In short, you can cancel an event with printed cost X (including another The Hand's Judgement) with "The Hand's Judgement (Core)" at no cost, regardless of how much gold was spent as part of the cost of the event you are cancelling.