He said that he presumed that I was one of the Pinkerton's men.
It is proper indirect speech, there is no need to worry.
In the textbook the indirect speech is given as 'He said that he presumed me as one of Pinkerton's men'
Usually, there are several ways to tell the same thing. It is the same here. The book is also right.
However, it would be better to say:
He said that he presumed me to be one of Pinkerton's men.
so the book is not completely right.
I doubt about the use of two 'that' in my version of indirect speech.The use of second 'that' is making me to doubt about.
Although it might not sound perfect, it is still correct to use "that" twice in a sentence.