Seems we're dancing around the issue a bit. So how about some definition:
If its a bribe or kickback, the OP has to decide if they want to do business that way. I don't, never have, but its not unheard of. Participating in it has its benefits (you get to play) at the cost of bad ethical position. The relationship of ethics to business practice have been well studied over many years:while good ethics can be costly in a bad scenario, they are supposed to be worthwhile. Each their own. Its only been a debate for the past three millenia. People do illegal things for all sorts of reasons.
- if its a "discount", then its quite possibly a reasonable position to be discussed: "you were bought directly, will you lower your price?". There is a reasonable, if unpleasant, reality here - it might be true, it might be worthwhile.... if business is slow, people will negotiate prices. Some never do... but some do. That's not necessarily wrong, and is certainly a point that one can discuss and ethically participate in.
Sussing out the difference between these two is the delicate part. If the client is willing to accept an invoice that shows clearly the reduction in price, then its a negotiation. If the AD wants it off the top, on the side, in cash.... then its clearly something else.
One way to handle this is to move discussions from the first category into the second: offer to write up the invoice with a discount, thus showing willingness to accept the reduction in price, but an unwillingness to participate in something off the books (and likely illegal and immoral). Often, if handled carefully, the request will disappear, amidst quiet embarassment.
That the request is wrong is not to deny that it sometimes happen. Less these days than it used to... and yet probably not unheard of. I'm not condoning it in any way, but just acknowledging the dilemma the OP put up. Its ugly, big league. The short answer is find different clients. The longer answer is to try to move the request from the back room into the light of day, where it can be addressed legitimately.
Geoff