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<<Because of the layout, the team believes users won't have a problem
figuring out which of the identically-named controls to select.>>
If it is a good UI design and the users won't have trouble, then why change it?
What you are describing sounds similar to Word's Organizer dialog box for templates (to find it, go to Tools>Templates & Add-ins and click the Organizer button). There are two fields called "Styles available in" and two Close File buttons. It is very obvious to me which Close File button goes to which file because of the placement of the buttons.
Like most other things, you can't make a hard and fast rule about never using the same name on two controls on the same screen. Sometimes it works and sometimes it doesn't. When multiple controls have the same name, the screen is harder to document, but if the screen is usable, then users won't be turning to the documentation anyway <g>. Focus your discussions with the user interface design team on things that are real usability issues not documentation issues. You will earn much more respect and perhaps be invited to be part of the design process earlier on.