It is a lot easier for a buyer to get out of a contract than a seller. If the seller needed to get financing to make this happen, I would say the most proper way I know to have handled that situation is to write it in as a contingency on the counter offer.
For example: This counter offer is contingent upon the seller obtaining financing to pay off the current mortgage and/ or any additional liens on the property.
Was something like that in the counter offer? Just curious. Otherwise it seems like you have a great case, but then again I am not an attorney. Again I suggest that you get an good real estate attorney. Who knows maybe a letter from an attorney will put things into perspective for the seller:)
I hope this information helps! Best Wishes!