I think that on those other machines (or your's), a different Wingding font is being used. Did your tech people check that there aren't multiple wingding fonts on the machines? The Mac OS will put fonts in several places. In a font folder in your “system” folder, a font folder in your “library” folder, in your “user's library font folder, and Microsoft has it's own set of fonts as well.
Have your tech people checked the path of the wingding on each computer?
By that, I mean, when it's working on your machine have them go to “Type” then scroll down to “find font.” Click on the wingding font and get more info and check the path name. Then for the troublesome machines, if they need to change to their font, have them change it to their winding and have them check the path.
I really think it's an issue of a different version of the wingding on the problem machines or duplicate fonts, and not an InDesign problem.
Have you cleared font caches?
Are you using any font management apps, like Suitcase?
At my company we use Suitcase and Fusion and really manage our system and user folders, and keep them to a bare minimum. We put the fonts for each job into a separate folder within that job. If we ever get issues like your's, it's simple to easily follow the path to that individual font folder.