Home Improvement Questions? Ask a Handyman for Answers
A repair generally doesn't require a permit. An entirely new roof does. $3k isn't outrageous for this if it is done properly which means ripping off all the old roofing material and replacing it.
The permit is HIS responsibility not yours. Permit requirements vary by locale. I said generally because I don't know where you are and I don't know the requirements for every jurisdiction in the country. In any event he can't hold no permit over your head because it's his responsibilty to get one if it's required. I'm not lawyer and this is not a legal opinion but I don't see how he has any claim at all that will hold up in court. If anything based on what you've told me you should sue him!
I don't know what the requirements are in SF. Your best bet to find out is to call the local code enforcement/building inspector's office and ask if a permit is required for a roof repair of the size (give them square footage) you have. You don't have to give your name. I do know that contractor's in CA are requird to be licensed and not pulling a permit can be cause for license revocation. The inspectors are there to protect you. Contractors who threaten legal action to extort money out of clients when they didn't perform the agreed upon work are despicable and give us honest contractors a bad name.