Countrywide does require a prospective purchaser making an offer on their properties to be pre-qualified with them. (They cannot make you go through them for the new loan but the will offer in many cases a free appraisal and credit report as well as a competitive rate that should meet or beat anyone els's in many cases if you do get the home and take the new loan through them.)
I am on "CW"s approved Realtor list and work with them with their REO's so I have some experience here.
They will also not "Formally Counter" your offer in many cases. The decision that you need to make is: Is it worth the list price to you or not? There are various ways to value a property. A "Buyers Agent" could have helped with that but as one other agent noted in his response (It's too late for that now.) What you can do is hire an independent appraiser of your own to appraise it in "As-Is" condition for you to feel better about the home and the final negotiated price, but in the meantime, other buyers are looking at the home and can sneak in and get an offer accepted while you are doing your due dilligence. Expect to pay anywhere between $300 & $400 for this service (Especially if its a rush.)