your AWD brings up specific rate codes, and specific rate codes are awd dependent. The website allows for rate codes for the use of certain travel agents booking (some have certain awd's and three or four rate codes that will work on that one awd).
The computer will always give you the lowest rate that you qualify for based upon the available information. When you log in with your profile, it knows that you qualify for the AWD A1111111 or whatever awd you use. if you want to use a specific awd, remove your old awd and put your awd in there (profile update) see the price and then move it back or do what you did and dont use your normal method for accessing it. Or you can just call avis.