I would tend to agree with the advice given so far that you should bail on the well-known company, but you also need to tell them directly why it is that you ar

I would tend to agree with the advice given so far that you should bail on the well-known company, but you also need to tell them directly why it is that you are no longer interested in their offer. It is possible, but unlikely, that they will adjust the offer, but they need to know that they made a mistake so that they can correct in the future.