You are mistaken. If the work is distributed under a license, then you have no right to use the work except under the terms of the license. The license acts like a contract.
If the law did not work that way, then the GNU GPL would not be enforceable.
The GPL for example required that if I distribute a derivative of a GPLed work in binary form, then I must also distribute the same derivative as source code or at least provide the source code to any distributee who asks for it. This requirement of the GPL has been enforced by courts (e.g., in a lawsuit against Tivo) even though none of the defendants in these court cases signed a contract regarding the use of the software.
> The GPL for example required that if I distribute a derivative
So, in other words, if you don't distribute a derivative work you are fine.
Like I said. The point stands once again. Everything that you said only applies for distribution of copies. And if you don't distribute copies, and you don't sign any contracts, you are fine.
> This requirement of the GPL has been enforced by courts
You have misunderstood that court case. Nobody can be forced to follow the GPL. Instead, you can only be forced to pay damages for distributing copies.
Following the GPL is simply a method of avoiding damages for distributing copies. But you don't have to follow it. You can simply either not distribute copies, or you can pay damages for your distribution of those copies.
So the point stands once again, that you cannot be forced to follow these contracts, and you can only be prevented from distributing copies.
The AGPL says that you cannot use a derivative work of the licensed work to operate a server on the internet without releasing the source code of your derivative work. Since the server operator is not distributing the licensed work or any derivative of it, then according to you the AGPL has no legal force and can just be ignored. Ditto no-commercial-use licenses.