Thanks. Based on your feedback, I plan to turn down the offer unless the agreement is changed.
Regarding the identity of the company: I am concerned about embarrassing the company publicly. I can email it to you directly. It is possible that this is not a typical agreement at the company. I would be working in a group where IP is of greater than usual concern.
EDIT: Mailed to you at ycombinator.com with my account name in the body.