"Is it possible for some skyteam members to have better access to other members inventory than the rest? If not, how do I explain this to the DL reps?"
Yes!
and
You do not. even if they are informed enough to understand it there is nothing they can do about it.
All carriers always have the best availability for members of their own programs. Marketing partners only have what they decide to give them. However, in some rare cases you will find DL availability on on the NWA website. Usually when I have had this happen and want the flight the DL rep creates a seat on the DL side as a courtesy.
This is not my opinion, it is based on my experience. Just recently I wanted to go AMS-CPH KLM. On the nwa site it indicated all flights had BIZ class (EUROSELECT) available for saver awards, when I called DL to book only the 10:30am showed up. Luckily for me that was exactly what I wanted.
Saw the same thing on CO a few years ago DL had seats for skymiles but, CO could not access them for use with CO FF miles.