I think the Egyptians had already entered their Imperial twilight years.
They may have exerted some influence over the land of Canaan, but I don't think they dominated it.
However, it's a fair point!
If you click on the first link on this page, the book comes up.
Scroll down to pages 59-61.
Quite a while since I read it, but it's a very interesting book overall. Plenty of detail without being too heavy!