Sounds like you might not be working with realtor?
I've assisted serveral buyers with foreclosures in the last year and what I've found that the person on the negotiation side for the bank usually does not make their decisions based on the buyers credit. Although, it will definatley be a factor when your bid is accepted. If for some reason the winner will not be able to qualify then the bank usually drops that bidders offer and moves on to the second offer. Also, keep in mind that just because there is another offer does not always mean they are competing offers. The other offer might be offering full price but asking for down payment assistance and/or closing costs which would effect the banks bottom line.
As I tell all my buyers you should always make your best offer first (whether it's a foreclosure or not) because you might run the risk of loosing the home to someone else who wants the house just as bad and has made their best offer. If the home has been on the market for quite a while without any drop in price then make a lower offer but beware that if it's too low you might not even hear back from the lender!
Hope this helps! And call one of your local realtors so they can help you through the process, it's a jungle out there!
Karen Taylor ERA Chamberwood Realty