I totally get what you are saying. Though, when that one Wilcoxon test is the same as the Mann-Whitney test, does it matter which one you write down?
The problem in the book is that for dependent samples they only say "Wilcoxon" which is poor form on their part because there are two "Wilcoxon" tests: the Wilcoxon rank sum (same as MW, and is for independent samples) and the Wilcoxon signed rank test (dependent samples).
For someone who needs the flow chart or in an introductory class, they are less likely to know the difference and that the chart means the Wilcoxon signed rank test for dependent samples. If this student just knows "Wilcoxon" for dependent and has to actually use this knowledge later, they might be confused and incorrectly select Wilcoxon rank sum (which is another name for MW) when they meant Wilcoxon signed rank (all the book needs is to add two words "signed rank").
The book also suggests that parametric and nonparametric methods should be chosen based on the p-value of a normality test, which is also poor form.