It's not ridiculous. The standard advice to anyone who hires a contractor is to get a W-9 before any work begins.
My advice to you is to give them the W-9. If I were the law firm I would insist on getting the W-9 before you started any work, and I certainly would not pay you anything until I got a W-9 from you. They don't want to worry about having a hard time getting a W-9 from you if you should happen to do more work for them and they end up paying you $600 or more for the year. Contractors are not always cooperative about providing a W-9 after they have been paid.
I would find it reasonable for a client to reject any independent contractor who would not provide them with a Form W-9. In addition to providing the client with your TIN, Form W-9 also provides your certification that you are not subject to backup withholding, that you are a U.S citizen or U.S. person, and whether or not you are exempt from FACTA.
It's perfectly normal for anyone hiring a contractor to ask for and require a W-9 before they will hire you, or pay you. If you are self-employed then you should provide them your business EIN. If your business does not have an EIN, there's no reason for not getting one for your business right now. It's absolutely free and takes less than 10 minutes on line starting at https://www.irs.gov/businesses/small-businesses-self-employed/apply-for-an-employer-identification-number-ein-online