Decoding problem and conditional probabilities
Maximizing $P(r|t)$ is known as the Maximum Likelihood (ML) principle, while maximizing $P(t|r)$ is known as the Maximum A Posteriori probability (MAP) principle. 

Here are some facts that answer your question: 


Optimal decoding (minimizing the probability of error) is achieved by the MAP principle. See p. 152 of the book.  
However, using MAP would require a different decoding algorithm for every distribution on $t$. I.e. you would have to adapt decoding to the statistical properties of the source. To avoid this, it is typical to assume a uniform distribution on $t$. In this case, MAP and ML are equivalent because $P(t|r)$ becomes proportional to $P(r|t)$ (see p. 152 again). 
I agree with you he should have started with the MAP problem of maximizing $P(t|r)$, since that's the correct goal anyway. But I presume that he is assuming a uniform distribution on $t$, in which case the difference doesn't matter anyway.