Dear Dave: I called a creditor recently to settle an old debt. They offered a settlement but said it was their policy not to put settlement offers in writing. Should I accept the deal?
No way. If you don't have anything in writing, then you have no proof that they extended the offer or agreed to a specific amount. The only one who will have "proof" of anything in this scenario is the creditor, and that's just asking for trouble.
My suggestion for handling this ridiculous situation goes something like this. Explain to them that you seem to have reached an impasse, because you have a policy of never accepting settlements and handing out money unless the settlements are in writing. No writing, no money! It's not a hard concept to understand, and it's fair to both parties.