Gail,
If you don't think it was their intention to buy both properties, the dilema and responsibility might fall with the lender. If they are making multiple offers before one is accepted, then they appear to be commiting fraud, from my perspective, unless they qualify for both purchases.
In my market, I couldn't possibly consider writing a purchase offer without Desktop Underwriting approval. My lender is providing the seller information on his/her ability to buy the property based on the information given to her by the buyer. If the buyer didn't give the lender the "information" that there was another offer on another property, then the onus falls on the buyer. FRAUD at loan application. I'm sure it might not be as competitive in other areas and might not require a lender letter, but in my area, my lender would be toast if she intentionally wrote two letters of approval that were in essence, BS!