I"m coming into this a little late, but personally, I'd move on. It's only good business to sign a contract and if they consider it too much of a hassle my gut feeling is that you'll find yourself having some kind of issue down the road and no recourse because there wasn't a contract signed between you and the client.
To me, this appears more like they are just looking for people to work as "employees" but call them "independent contractors" to save themselves the extra paperwork and monitoring for taxes etc....
If someone doesn't want to work with you based on terms you've set or mutually agreed upon then in my opinion they are calling the shots and it's your decision whether or not you work with them, not the other way around. As a business owner you have that choice and power.