That particular entry does muddy the waters somewhat. However, it is important to note that nowhere in the rules is "target" defined as "the object and/or recipient of an ability's effect." That can't be the definition of "target" for the game because:
- Not all objects and/or recipients of an ability's effect are considered "targets" of that ability. An ability can affect a game element without having a "target."
- Not all chosen "targets" are directly affected by the ability in question. Sometimes, an ability's chosen target(s) serve as references to tell you how the ability resolves (as with To The Rose Banner!, using its target to define X, and Wildfire Assault, using its target to define which characters are killed by exception rather than by direct choice).
The actual definition of "target" from the rules ends up being "a game element that must be chosen (by the player resolving the ability) in order for an ability to resolve." This ends up encompassing both direct targets (i.e., game elements chosen as the objects affected by the ability's effect), and reference targets (i.e., game elements chosen to define the scope and resolution of the ability's effect, but not actually affected by the effect itself).
And that's the problem here. The entry on targets in the RRG does NOT make a distinction between direct and reference targets - even though the cards clearly do. As such, the fact that the bit about "A card is not an eligible target for an ability if the resolution of that ability's effect could not affect the target at all." applies to abilities with direct targets, but not to abilities with reference targets, is completely lost.
The plot chosen as a target for Pulling the Strings is a reference target (similar to the characters chosen by To the Rose Banner! and Wildfire Assault), so the entry in the RRG about eligible targets needing to be affected by the ability doesn't apply to it - because NO PLOT CARD would ever be affected by the effect of Pulling the Strings. As such, you could choose Noble Cause in the above example and let there be no affect on the game state. (Note: the rule about "a card ability can only be initiated if its effect has the potential to affect the game state" doesn't apply here because the game will trigger/initiate the "When Revealed" ability of the plot no matter what; and you are only obligated to choose an eligible target - not necessarily an eligible target that would allow the ability, which has already initiated, to resolve successfully.)
Now, admittedly, this whole discussion about direct vs. reference targets, and the inapplicability of the "A card is not an eligible target..." rules text to reference targets is nowhere in the rules documents. Rather, it is a general explanation offered to allow the card text of things like To the Rose Banner! and Wildfire Assault to work period - because a literal reading of the rules without such an explanation/understanding of the existence and role of "reference targets", these cards would not work at all. There is a basic assumption that cards are not written so as to not work at all, so I offer this as a means of answering questions like the OP related to Pulling the Strings until we get something official from FFG.