Understanding Alpha Beta Pruning: Why do we ignore the values of a unsearched tree after the first leaf, can they not include acceptable values too?

So this is my question.

I am trying to understand this part of the book:

At d) why do we stop looking at the other nodes in that branch? There could be a acceptable value next to the 2? I am just trying to understand alpha beta pruning for a while.

At $d)$, minimizer is comparing the $2$ he found with the currently best option for the maximizer higher in the tree (at node $A$, where maximizer will choose between $B$,$C$,...), which is $3$, at node $B$. He then knows that maximizer will not choose $C$.
The node $C$ will have value $2$ when minimizer sets it and would have value $2$ or less if minimizer explored it fully, so he doesn't need to waste his time searching other branches from $C$ if he already knows that maximizer will not choose anything lower than $3$.
So there is no way that minimizer could in this situation "fool" maximizer by setting the wrong value of $C$ (something higher than $3$) to force maximizer to choose it. If we assume that scenario a possibility, we must also implement the maximizer with "free-will" so he may not choose his best option but this is no longer an $\alpha$-$\beta$ pruning :)