Josiah al-Hasan ben Zakkai - Father Seems Wrong

To amplify, here is a 12th Century pedigree of Josiah ben Zakkai:

"The elaborate genealogy copied down by Abraham al-Raḥbī sometime in
the twelfth century is similarly arranged. Torn at the top and thus missing
the personal name of the nasi for whom it was composed, the ancestor list
runs as follows:
. . . son of . . . Zakkay . . . son of Joseph, son of Zakkay, son of ʿAzarya,
son of Solomon, son of Josiah, son of Zakkay, son of Judah, son of
David, son of Judah, son of Isaac, son of Solomon, son of Ḥisday, son of
[Ba]radoy, son of Bustani, son of Rav Ḥuna, son of Kafna[y], ..." From This Noble House by Arnold E. Franklin, p 76.

As can be seen, there are significant differences between the 12th Century pedigree and what is shown on GENI. Most notably, Zakkai is missing as the father of Josiah and his brother David on GENI and then above the ggf level, the names do not come close to matching. The descent from Josiah does match well on both trees.