Taxonomy inheritance from Product to Product Display

Googled this a bit but unclear if a resolution has been identified yet...

Product has taxonomy (call it Brand).
Product Display uses Product Reference field to display Product details. Here the Taxonomy Term (Brand) is visible.
When viewing the Brand Term Taxonomy Page no content is identified as tagged by that term.

** Is it possible to for Product Displays to inherit terms from Products? **

I see the hierarchy as this:

         --View, etc --
    --- Prod Dis ---
---- Product Def ----

----- Taxonomy Term -----

IE: Taxonomy is the foundation. The Product draws in the various taxonomy terms as directed (EG: Category, Brand, Product Uses). The Product Display then in turn inherits attributes from the Product Definition and the Taxonomy Terms.

The role of the product display is to merely provide different formatting, product (granular) bundling and editorial/stylistic options.

Comments? Thoughts? How to achieve this without requiring entering Taxonomy on both Product and Product Display?