Sure, you could argue that...
But look at it from their perspective. If they have the domain, they still get the traffic, but don't have to pay you a commission. Why should they pay a commission to somebody who is trading off of their good name?
One can argue that they would never have thought of that domain name. They may be thinking that themselves - and it may be why they are willing to make you an offer. Perhaps they are willing to compensate you for the novelty of thinking-up the domain name, even though it may be confusingly-similar to theirs.
Yes - see a lawyer - a GOOD one is not going to drag you into an unreasonable position that is going to be costly to defend. He should level with you, tell you what (if any) laws you have violated, honestly state your prospects, and look out for your interests in any negotiations.
Of course, the right time to see a lawyer was when you dreamed-up this name. Again, WHAT were you thinking?
That's not a retorical question. I'm curious as to what line of thinking went into this domain name and how you have used it, as well as your not notifying the company that you were using this name to send them affiliate traffic. Many affiliate programs require you to disclose domain names when you sign up - does yours?