The document “Example.dmg” could not be opened. Disk Utility cannot open files in the “Disk Image” format
So, this solves the problem of how to get the file to open. I don't know why the "open with" was not working, but after several hours of trying different search strings in Google, I found this article that explains how to change the default to the disk image mounter instead of the Disk Utility: How to change default apps on the Mac.

Steps are copied below:


Go to the Mac's Finder.
Find the file type you'd like to open with a specific app, and select it.
Click on the File menu and select Get Info.
Expand Open with: by clicking on the triangle to the left.
Select the Open with: menu, then choose the app you'd like to use to open all documents like that one.
Click the Change All... button.
You'll get a dialogue box asking you to confirm your choice. Click Continue.
Close the Get Info window.


Worked like a champ.  I don't know how this got changed in the first place (my Macbook did not change), but that is another question.