Acceptable for what? For practical engineering purposes it would usually perfectly acceptable. The difference between the two values is less than 1%.
The book is making more "precise" assumptions (see the plot of the shear distribution in Fig. e) but the author might have "forgotten" that all of this mathematical theory is based on approximations (Euler-Bernoulli-Timoshenko beam theory) in any case!
The "correct" answer depends on exactly how the shear loads are applied to the beam and how it is supported - both of which are ignored in the book example.
Of course in some situations you might need to do a full 3-D finite element analysis of the hollow structure to get even more details of the stress distribution - but that would be pointless if it is just being used as a structural beam and you don't know exactly how it is loaded and restrained.