The book has good stuff when it comes to the history of the monument through the ages and descriptions of the mausoleum itself.
The author however is forging a pre conceived conclusion based on the religious inclinations in effect before, during and after the Mughal period.
No mention of Anarkali in the references available from the king's scribe does not mean that she never existed. Akbarnama and Jahangirmana where written during the respective kings lifetimes and thus presumed to be heavily biased towards the kings themselves. Putting an illicit relationship in black and white would greatly undermine the positive aspects of the ruling kings and their influence.
At the same time, the mausoleums of the Mughal queens mention their names in the majority of the cases. If Sahib Jamal was Jahangir's beloved wife and he erected a tomb for her, why her name was never put on the tombstone?
There are only a few references available about Anarkali and they cannot help in an objective research. Since we have a lot of penned down history for the Mughal era, my assumption is that it is what we have and sadly it is without any direct reference to Anarkali's existance.
Jahangir in an illicit relationship with his step mother or Anarkali being Akbar's favourite harem girl could be the reasons for her not showing up in the memoirs.
