IANAL, but I don't see why this would not hold up. It is their code, its in their license agreement (which is a contract you agree to). If you do not wish to give them the rights to your modifications, the license forbids you from using it
Sure, but I was of the impression that they can only control rights to use their software, not claim your own - I'm not sure if "which is a contract you agree to" is true if nothing is signed.
Note: by reading this notice you agree that all that is yours is mine, and all that is mine is mine also. ;-)
Your note does not work because I am not agreeing to anything. You either are agreeing to the license implicitly by using the product, or you are not allowed to use it (and would therefore use code which you dont have a license to)
Well it's an option - either you follow the terms of the license agreement and give up ownership, or you're in violation of their copyright. (Or you contact them and work out better terms.) They can put any terms they want in the license agreement, if you don't agree to them you don't get a license.
Think of it with money instead. If they charge $20 for a license, then you have the option to pay, or to be in violation of copyright. Here they're requiring a transfer of IP instead of money but it's the same deal.