Why is BuLi a better nucleophile than base?
This is a trick question, which explains why the first sentence from the book takes so many precautions. It is very difficult to provide a general explanation because there are many factors influencing the result.


Solvent: the solvent is extremely important in such reactions. It
plays an important role in the order of oligomerization of the
organolithium reagent; monomers, dimers, tetramers or polymers. Of
course, the reactivity is really different.
Co-solvent: a co-solvent like HMPT or TMEDA can drastically change
the course of the reaction by changing the order of oligomerization.
Temperature: it is well known that n-butyllithium is a very strong
base at low temperatures (&lt;-60°C) but will become a good nucleophile
at higher temperatures. It can even open a THF ring.
Thermodynamic or kinetic control: organolithium compounds are
usually used under kinetic control, but...
HSAB: how the oligomerization affects the hardness/softness of the
base and its nucleophilicity?
3D shape of the organolithium compound: it greatly influences the
shape and order of oligomers.
...


So now you feel completely depressed, I can try to answer your question. I think that a key factor is actually that in a cluster (dimer, tetramer and so on), charges are more diluted which enhances the nucleophilic behavior. Also, the geometry of the cluster and of its 3D-complex with the substrate could explain why a reaction is favored over the other.