Thanks, Rob! Yes, this is exactly how I'm using book and document numbering—and it's also the reason it is possible for a page to be shuffled as I move documents around in the book or add pages to a chapter as in your example.
The behavior is as expected (and as desired), since I want things to be reflowed/adjusted/renumbered throughout the book as individual documents move or change. The only thing I'd like to do is get some kind of warning when that correct behavior causes a "must-be-an-odd/even" page (of which there are only three in this particular book) to be shuffled to the wrong side of the spread. Then I can decide whether to resolve it by adjusting document order, manually adding a blank page, etc.
Edited to add: comparing your example to what I'm doing, let's say that Chapter 1 and Chapter 2 can start on any page (odd or even) but because of a full-spread illustration that spans pages 14 and 15, Chapter 3 absolutely must start on an odd-numbered recto. In the first image of your three screenshots, Chapter 3 starts on the correct page, so I wouldn't need or care about a warning that I had messed up the layout.
In the next two examples, where you've added pages to Chapter 1 and Chapter 2, Chapter 3 now starts on an even-numbered verso and the illustration will be split between spreads.
I want some kind of HEY DUMMY alert when that happens. But nicer. Like ... a preflight error. 
Hi Boris,
I think, I found a way using preflight for such a task.
In the category IMAGES and OBJECTS you could preflight if an object is in the margins.
You can define the values for the margins there as well.
The following screenshots from my German InDesign will show this:
1. Illustration on facing pages. No error in preflight.

2. Illustration on odd page only. Error in preflight.

Hint: It's not the big illustration that triggers preflight.
It's a small anchored frame that is running with the illustration and changing its place from inside to outside:

If I move it more inward, no preflight error:

Here my settings in German:

I think, that little trick should do it…
Regards,
Uwe