Did WaMu say who they sold the debt to?
How do you know that they are the legal holder of the debt?
You would be smart to send them a DV letter and make them prove that they are the proper company to pay. Asset is a Collection company and generally don't farm out the collection.
Don't worry about the settlement offer, they will make others and they will be better. They are trying to get you will you are unsure of what is going on.
If you pay the wrong company then it is an Oh Well, your out of luck because you will have to pay the rightful one.
CA's are not to be trusted. But if you are sending the payment overnight their signature of receipt is proof of timelyness. Make sure you do not waive deliver signature. Send them a money order NOT a personal check, regardless of what they say.
Contact them again and ask that they send you a signed statement saying that the debt will be settled in full and that the remainder will not be sold off. DO NOT send them the money without this agreement.
Also is their letter signed by somebody or is it a form letter with some department name at the bottom? If it is signed, is there a printed version of the name?