I'll try to make it clearer then.
As far as people reaching the site by entering one of the domain names it makes no difference which directs to which as both end up at the same place.
Where actual links only use the domain that the site is actually on those links go straight to the site as well.
The only time links would ever go to the domain that is redirected is if you changed which domain the site is on. The redirect is basically an instruction to say that the site used to be at that address but has now moved (301 means permanently moved) to the new domain. The domain being redirected should therefore be ignored as the address has changed. Ignoring the address being redirected is what 301 means. If you don't want it ignored you'd use 302 which indicates that the move is only temporary and the address will be changed back later.
So why would you expect the search engines to disregard a clear instruction "301 - ignore this address as it has been premanently changed"?
That being the case, you want the most descriptive of the names as the one that doesn't have the ignore/redirect associated with it.
Of course the search engines can "see" both domains - the difference is that one has an ignore/redirect command attached to it and the other doesn't. So the search engine does what it has been told to do and redirects to the replacement address.