Agreed, do not let your school's financial aid department push you around. The school has to allow you to get your loans through either their recommended lenders or one of your choice. So, for example, if your bank offers student loans, you could go through them if you wanted to. It's usually a bit easier to go with one of the recommended lenders because the school automatically approves the paperwork for the loan company (saves you a step) but if you don't mind doing a little extra legwork, you can go with whatever lender you'd like.
I've never heard of anyone having a good experience with Sallie Mae. Unfortunately, a lot of people who initiate their loans through other lenders end up with SM anyway because their loans get bought, but I stayed far away from SM for my law school loans and hopefully my lender won't sell me out. Just my two cents. I don't know that much about Access Group.