Seems to me like there's fault on both sides.
Firstly, the client provided the correct phone number, so it's reasonable for them to assume that it has been copied correctly. If it hasn't, it puts the blame firmly in the designers ball park.
On the other hand, a final proof was shown to, and signed off by, the client. In my experience the proof is to verify the entire thing, not just the design. Content can change from initial concept to realisation and therefore should be checked beforehand. However, as said before, the correct phone number was provided, and as they change very rarely, I think it's reasonably for them to have just glanced past that part.
I have had a client in the past who were using a temporary phone number when the contract was first signed which changed just before the final concept sign-off. They didn't pick up on the fact that the proof had their old number - however we did.
Unfortunately I think this may be a 50/50 situation. It's often not worth losing clients, no matter how small, as word of mouth spreads quickly and is often exaggerated. Point out to them that it's simply not reasonable for you to foot the entire cost of a reprinting as they DID sign off on the proof, even if they did supply the correct number, and try to negotiate an amicable solution for the both of you.