PageLab - thanks for that - I'll have to find out if it will work for the client's reading device. I suspect they want it to work on Android as well. But at least it's a possible fix.
amyg - It does this for tables too, and for images in tables, for some reason. I think the reason it does this for the text boxes is because those are formatted with an object style and not a paragraph style. It is a bit of a mystery for me because it does not do this when there are several text-boxes in a single InDesign document, just when it is set up as an InDesign book document, with several InDesign documents combined.