I am wondering if the writer of the book... a teen-ager... simply fell prey to the assumption that any Marmaduke Tatham must have been this Marmaduke Tatham's father...
It is my observation that, especially for this region and era, such an assumption is particularly invalid.
Looking at the parish registers of the region, there are so many Tathams, so many Wildmans...
I should confess thought that I was led to looking for other parents of Marmaduke because I found only only one baptized in his time.
https://www.geni.com/documents/view?doc_id=6000000182412900847
Yorkshire, England, Church of England Parish Records, 1538-1873 for Marmaduke Tathame
Thornton-in-Lonsdale, 1576-1812
Name: Marmaduke Tathame
Gender: Male
Record Type: Baptism
Baptism Date: 5 Apr 1619
Baptism Place: Yorkshire, England
Keyed Parish: Thornton in Lonsdale
Father: Roberte Tathame
Add this to the occurrence of another baptism in the same parish:
https://www.geni.com/documents/view?doc_id=6000000182381431930
and add these two circumstances to the fact that Elizabeth Tatham (who marrried a Wildman of Tatham parish) travelled in the same Quaker company that got into so much trouble with the Church of England...
Even though all this, which is reflected in the pedigree I have built here on geni, is not conclusive, I have to say that it is more conclusive than the 19th century pedigree assembled by Richard Ecroyd Tatham
The jury is still out on all of this...