Late yesterday, I finally solved this problem. (At build 378)
I said ...
If the disk's "ignore ownership" is CHECKED, however, then the owner of the sparsebundle file is always shown as the current user. (This seems odd.)
The man page for diskutil, enableOwnership verb, contains a complete explanation for the odd behavior, so this is no longer a problem.
I took a look at the source code for build 341 (6 Dec) and found that my problem was not "New Folder Needs Password", but was caused by the Finder command ...
set ignore privileges of diskAlias to false
This has always worked properly in the past, as it should, since I am writing code in an admin user. It failed because I began testing in a standard user. A standard user needs an admin password to execute this command.
A sparsebundle disk is created with the "ignore ownership" box checked by default. I think there are ways to uncheck this box, but they require 'sudo'. I am simply going to leave it checked. It's not a big problem. Any user that needs to change it and has an admin password can change it.
And the moral of this story: "Your code hasn't been tested until its been tested by a standard user."