Sorry, no. Fees are paid to the issuing bank, acquiring bank, and network. The majority of it goes to the issuing bank, and that's the non-negotiable rate when you get a merchant account. That fee is known as the interchange fee. The processing fee is something you negotiate with your gateway and/or acquiring bank.
It's great to know that you work in the industry, but it's irrelevant; argumentum ad verecundiam is a logical fallacy and only serves to demean your argument.
To address your point, I understand interchange as being set and collected by the card network, and is non-negotiable. Anything off the top is left for the banks to keep for themselves, e.g. the plus in "interchange plus" pricing). Another example assume a hypothetical interchange of 1.5% and a merchant that has a merchant account that costs 3.5% + 30¢ (gateway) per transaction. In this case the card network takes 1.5%, the gateway 30¢, and the banks 2%. Is this not how it works? It would be nice if you could cite something (not trying to be an ass in case it reads that way :).
I work in the industry; it's my job to know how this works. Here is an example from Wikipedia (bear in mind the amounts are fictitious but relatively accurate): http://en.wikipedia.org/wiki/File:Gao-report-on-interchange....